Progress in Materials Science 2008 Meyers

Biological materials: Structure andmechanical properties

Marc Andre Meyers *, Po-Yu Chen, Albert Yu-Min Lin,Yasuaki Seki

Materials Science and Engineering Program, Department of Mechanical and Aerospace Engineering,University of California, San Diego, La Jolla, CA 92093, United States

Abstract

Most natural (or biological) materials are complex composites whose mechanical properties areoften outstanding, considering the weak constituents from which they are assembled. These complexstructures, which have risen from hundreds of million years of evolution, are inspiring Materials Sci-entists in the design of novel materials.

Their defining characteristics, hierarchy, multifunctionality, and self-healing capability, are illus-trated. Self-organization is also a fundamental feature of many biological materials and the mannerby which the structures are assembled from the molecular level up. The basic building blocks aredescribed, starting with the 20 amino acids and proceeding to polypeptides, polysaccharides, andpolypeptides–saccharides. These, on their turn, compose the basic proteins, which are the primaryconstituents of ‘soft tissues’ and are also present in most biominerals. There are over 1000 proteins,and we describe only the principal ones, with emphasis on collagen, chitin, keratin, and elastin. The‘hard’ phases are primarily strengthened by minerals, which nucleate and grow in a biomediatedenvironment that determines the size, shape and distribution of individual crystals. The most impor-tant mineral phases are discussed: hydroxyapatite, silica, and aragonite.

Using the classification of Wegst and Ashby, the principal mechanical characteristics and struc-tures of biological ceramics, polymer composites, elastomers, and cellular materials are presented.Selected systems in each class are described with emphasis on the relationship between their structureand mechanical response. A fifth class is added to this: functional biological materials, which have astructure developed for a specific function: adhesion, optical properties, etc.

An outgrowth of this e!ort is the search for bioinspired materials and structures. Traditionalapproaches focus on design methodologies of biological materials using conventional synthetic

0079-6425/$ - see front matter ! 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.pmatsci.2007.05.002

* Corresponding author.E-mail address: [email protected] (M.A. Meyers).

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Progress in Materials Science 53 (2008) 1–206

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materials. The new frontiers reside in the synthesis of bioinspired materials through processes thatare characteristic of biological systems; these involve nanoscale self-assembly of the componentsand the development of hierarchical structures. Although this approach is still in its infancy, it willeventually lead to a plethora of new materials systems as we elucidate the fundamental mechanismsof growth and the structure of biological systems.! 2007 Elsevier Ltd. All rights reserved.

Contents

1. Introduction and basic overview of mechanical properties . . . . . . . . . . . . . . . . . . . . . 32. Hierarchical organization of structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73. Multifunctionality and self-healing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114. Self-organization and self-assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115. Basic building blocks (nano and microstructure of biological materials) . . . . . . . . . . . 12

5.1. Molecular units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.2. Biominerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2.1. Biomineralization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2.2. Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2.3. Morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.3. Proteins (polypeptides). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3.1. Collagen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3.2. Keratin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.3.3. Actin and myosin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.3.4. Elastin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.3.5. Resilin and abductin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.3.6. Other proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.4. Polysaccharides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.4.1. Chitin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.4.2. Cellulose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6. Biological ceramics and ceramic composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.1. Sponge spicules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.2. Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.2.1. Nacreous shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.2.2. Conch (Strombus gigas) shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.2.3. Giant clam (Tridacna gigas). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.3. Shrimp hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.4. Marine worm teeth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846.5. Bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.5.1. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.5.2. Elastic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.5.3. Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916.5.4. Fracture and fracture toughness of bone . . . . . . . . . . . . . . . . . . . . . . 94

6.6. Teeth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.6.1. Structure and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.6.2. Growth and hierarchical structure of elephant tusk . . . . . . . . . . . . . . . 103

6.7. Nano-scale effects in biological materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1056.8. Multi-scale effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7. Biological polymers and polymer composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1107.1. Ligaments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117.2. Silk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

2 M.A. Meyers et al. / Progress in Materials Science 53 (2008) 1–206

7.3. Arthropod exoskeletons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167.4. Keratin-based materials: hoof and horn . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

8. Biological elastomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1228.1. Skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1228.2. Muscle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1288.3. Blood vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

8.3.1. Non-linear elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1328.3.2. Residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

8.4. Mussel byssus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1348.5. Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

8.5.1. Structure and mechanical properties . . . . . . . . . . . . . . . . . . . . . . . 1358.5.2. Mechanical testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1378.5.3. Cell motility, locomotion, and adhesion . . . . . . . . . . . . . . . . . . . . 141

9. Biological cellular materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1469.1. Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1469.2. Wood. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1519.3. Beak interior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

9.3.1. Toucan and hornbill beaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1569.3.2. Modeling of interior foam (Gibson–Ashby constitutive equations) . . . 158

9.4. Feather. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16310. Functional biological materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

10.1. Gecko feet and other biological attachment devices . . . . . . . . . . . . . . . . . . . 16610.2. Structural colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

10.2.1. Photonic crystal arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17210.2.2. Thin film interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

10.3. Chameleon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17411. Bioinspired materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

11.1. Traditional biomimetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17711.1.1. Aerospace materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17711.1.2. Building designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17911.1.3. Fiber optics and micro-lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18011.1.4. Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18211.1.5. Water collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18411.1.6. Velcro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18411.1.7. Gecko feet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18511.1.8. Abalone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18611.1.9. Marine adhesives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

11.2. Molecular-based biomimetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19212. Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

1. Introduction and basic overview of mechanical properties

The study of biological systems as structures dates back to the early parts of the 20thcentury. The classic work by D’Arcy W. Thompson [1], first published in 1917, can

M.A. Meyers et al. / Progress in Materials Science 53 (2008) 1–206 3

be considered the first major work in this field. He looked at biological systems asengineering structures, and obtained relationships that described their form. In the1970s, Currey investigated a broad variety of mineralized biological materials andauthored the well-known book ‘‘Bone’’ [2]. Another work of significance is Vincent’s‘‘Structural Biological Materials’’ [3]. The field of biology has, of course, existed andevolved during this period, but the engineering and materials approaches have oftenbeen shunned by biologists.

Materials Science and Engineering is a young and vibrant discipline that has, since itsinception in the 1950s, expanded into three directions: metals, polymers, and ceramics(and their mixtures, composites). Biological materials are being added to its interests,starting in the 1990s, and are indeed its new future.

Many biological systems have mechanical properties that are far beyond those that canbe achieved using the same synthetic materials [3,4]. This is a surprising fact, if we considerthat the basic polymers and minerals used in natural systems are quite weak. This limitedstrength is a result of the ambient temperature, aqueous environment processing, as well asof the limited availability of elements (primarily C, N, Ca, H, O, Si, P). Biological organ-isms produce composites that are organized in terms of composition and structure, con-taining both inorganic and organic components in complex structures. They arehierarchically organized at the nano, micro, and meso levels. The emerging field of biolog-ical materials introduces numerous new opportunities for materials scientists to do whatthey do best: solve complex multidisciplinary scientific problems. A new definition ofMaterials Science is emerging, as presented in Fig. 1a; it is situated at the confluence ofchemistry, physics, and biology. Biological systems are subjected to complex constraintswhich exhibit specific characteristics shown in Fig. 1b. The modified pentahedron pro-posed by Arzt [5] has five components: self assembly, ambient temperature and pressureprocessing, functionality, hierarchy of structure and evolution/environmental e!ects. Theyare specific and unique to biological materials. Biological systems have many distinguish-ing features, such as being the result of evolution and being multifunctional; however, evo-lution is not a consideration in synthetic materials and multifunctionality still needsfurther research. The schematics shown in Fig. 1b are indicative of the complex contribu-tions and interactions necessary to fully understand and exploit (through biomimicking)biological systems.

Some of the main areas of research and activity in this field are

• Biological materials: these are the materials and systems encountered innature.

• Bioinspired (or biomimicked) materials: approaches to synthesizing materials inspiredon biological systems.

• Biomaterials: these are materials (e.g., implants) specifically designed for optimum com-patibility with biological systems.

• Functional biomaterials and devices.

This overview will restrict itself primarily to the first two areas. Using a classical ‘mate-rials’ approach we present the basic structural elements of biological materials (Section 5)and then correlate them to their mechanical properties. These elements are organized hier-archically into complex structures (Section 2). The di!erent structures will be discussed inSections 6–9. In Section 11, we provide some inroads into biomimetics, since the goal of


materials engineering is to utilize the knowledge base developed in materials science to cre-ate new materials with expanded properties and functions.

Although biology is a mature science, the study of biological materials and systems byMaterials Scientists and Engineers is recent. It is intended, ultimately:

(a) To provide the tools for the development of biologically inspired materials. Thisfield, also called biomimetics [6], is attracting increasing attention and is one of thenew frontiers in materials research.

(b) To enhance our understanding of the interaction of synthetic materials and biolog-ical structures with the goal of enabling the introduction of new and complex systemsin the human body, leading eventually to organ supplementation and substitution.These are the so-called biomaterials.

The extent and complexity of the subject are daunting and will require many decadesof global research e!ort to be elucidated. Thus, we focus in this overview on a number

Fig. 1. Schematic representation of (a) contributing scientific fields and (b) constraints/components in the studyof biological systems (modified from Arzt [5, p. 1246, Fig. 1]).


of systems that have attracted our interest. This is by no means an exhaustive list, and thereare many systems that have only been superficially investigated. We are currently investi-gating: abalone [8,9], conch [10,11], toucan beaks [12,13], and crab exoskeleton [14]. We

Fig. 2. Ashby plots for biological materials showing (a) elastic modulus and (b) strength as a function of density(from Wegst and Ashby [17]).


add the silica spicules, that have been studied and extensively described by Mayer andcoworkers [6,7], as well some other selected systems.

Mechanical property maps [15], more commonly known as Ashby maps, have become aconvenient manner of concentrating a large amount of information into one simple dia-gram. The first such map was proposed, for metals, by Weertman [16], and thereforethe name Weertman–Ashby is sometimes used. They constitute a valuable design tooland have been extended to biological materials by Wegst and Ashby [17]. Thus, theyare a good starting point for this overview. Two maps are presented in Fig. 2; they presentthe Young moduli and strength as a function of density. There are several striking anddefining features:

(a) The density of natural (biological) systems is low. It rarely exceeds 3, whereas syn-thetic structural materials often have densities in the 4–10 range.

(b) There is a broad range in Young moduli all the way from 0.001 to 100 GPa. Thisrepresents five orders of magnitude.

(c) The range of strengths is almost as broad as the Young moduli, varying over fourorders of magnitude: 0.1–1000 MPa.

(d) There is an absence of metals, which require for the most part either high tempera-ture or high electric current processing. Nature does not have at its disposal thesevariables.

Wegst and Ashby [17] classify biological (natural) materials into four groups, indicatedby ellipses in Fig. 2:

Ceramics and ceramic composites: these are biological materials where the mineral com-ponent is prevalent, such as in shells, teeth, bones, diatoms, and spicules of sponges.

Polymer and polymer composites: examples of these are the hooves of mammals, liga-ments and tendons, silk, and arthropod exoskeletons.

Elastomers: these are characteristically biological materials that can undergo largestretches (or strains). The skin, muscle, blood vessels, soft tissues in body, and the individ-ual cells fall under this category.

Cellular materials: typical are the light weight materials which are prevalent in feathers,beak interior, cancellous bone, and wood.

In this overview we will follow this classification since it enables a logical and tractabledescription of very broad classes of biological materials. A considerable number of booksand review articles have been written on biological materials and they constitute the foun-dation necessary to embark in this field. Some of the best known are given in Tables 1 and2, respectively.

2. Hierarchical organization of structure

It could be argued that all materials are hierarchically structured, since the changes indimensional scale bring about di!erent mechanisms of deformation and damage. How-ever, in biological materials this hierarchical organization is inherent to the design. Thedesign of the structure and material are intimately connected in biological systems,whereas in synthetic materials there is often a disciplinary separation, based largely on tra-dition, between materials (materials engineers) and structures (mechanical engineers). We


illustrate this by three examples in Figs. 3 (bone), 4 (abalone shell), and 5 (crabexoskeleton).

In bone (Fig. 3), the building block of the organic component is the collagen, which is atriple helix with diameter of approximately 1.5 nm. These tropocollagen molecules areintercalated with the mineral phase (hydroxyapatite, a calcium phosphate) forming fibrils

Table 1Principal books on biological materials and biomimetism [only first author listed]

Author Year Title

Thompson [1] 1917 On Growth and FormFraser [18] 1972 Keratins: Their Composition, Structure, and BiosynthesisBrown [19] 1975 Structural Materials in AnimalsWainwright [20] 1976 Mechanical Design in OrganismsVincent [21] 1980 The Mechanical Properties of Biological MaterialsVincent [3] 1982 Structural BiomaterialsCurrey [32] 1984 The Mechanical Adaptations of BoneSimkiss [22] 1989 Biomineralization: Cell Biology and Mineral DepositionLowenstam [31] 1989 On BiomineralizationByrom [23] 1991 Biomaterials: Novel Materials from Biological SourcesFung [24] 1993 Biomechanics: Mechanical Properties of Living TissuesFung [25] 1990 Biomechanics: Motion, Flow, Stress, and GrowthFung [26] 1997 Biomechanics: Circulation 2nd editionFeughelman [27] 1997 Mechanical Properties and Structure of Alpha-keratin FibersGibson [28] 1997 Cellular Solids: Structure and PropertiesMcGrath [29] 1997 Protein-based MaterialsElices [30] 2000 Structural Biological MaterialsMann [7] 2001 Biomineralization: Principles and Concepts in Bioinorganic Materials ChemistryCurrey [2] 2002 Bones: Structure and MechanicsRatner [33] 2004 Biomaterials Science: An Introduction to Materials in MedicineForbes [34] 2005 The Gecko’s Foot

Table 2Principal review articles on biological materials and biomimetism [only first author listed]

Author Year Title

Srinivasan [4] 1991 Biomimetics: Advancing man-made materials through guidance from natureMann [35] 1993 Crystallization at inorganic–organic interfaces: Biominerals and biomimetic

synthesisKamat [36] 2000 Structural basis for the fracture toughness of the shell of the conch Strombus gigasWhitesides [37] 2002 Organic materials scienceMayer [38] 2002 Rigid biological composite materials: Structural examples for biomimetic designAltman [39] 2003 Silk-based biomaterialsWegst [17] 2004 The mechanical e"ciency of natural materialsMayer [40] 2005 Rigid biological systems as models for synthetic compositesSanchez [41] 2005 Biomimetism and bioinspiration as tools for the design of innovative materials and

systemsWilt [42] 2005 Developmental biology meets materials science: Morphogenesis of biomineralized

structuresMeyers [43] 2006 Structural biological composites: An overviewMayer [44] 2006 New classes of tough composite materials – Lessons from nature rigid biological

systemsLee [45] 2007 Nanobiomechanics Approaches to Study Human Diseases


Fig. 3. Hierarchical organization of bone.

Fig. 4. Hierarchy of abalone structure. Clockwise from top left: entire shell; mesostructure with mesolayers;microstructure with aragonite tiles; nanostructure showing organic interlayer comprising 5 wt% of overall shell.


that, on their turn, curl into helicoids of alternating directions. These, the osteons, are thebasic building blocks of bones. The volume fraction distribution between organic and min-eral phase is approximately 60/40, making bone unquestionably a complex hierarchicallystructured biological composite. There is another level of complexity. The hydroxyapatitecrystals are platelets that have a diameter of approximately 70–100 nm and thickness of!1 nm. They originally nucleate at the gaps between collagen fibrils. Not shown is theHaversian system that contains the vascularity which brings nutrients and enables form-ing, remodeling, and healing of the bone.

Similarly, the abalone shell (Fig. 4) owes its extraordinary mechanical properties (muchsuperior to monolithic CaCO3) to a hierarchically organized structure, starting, at thenanolevel, with an organic layer having a thickness of 20–30 nm, proceeding with singlecrystals of the aragonite polymorph of CaCO3, consisting of ‘‘bricks’’ with dimensionsof 0.5 vs. 10 lm (microstructure), and finishing with layers approximately 0.3 mm(mesostructure).

Crabs are arthropods whose carapace is comprised of a mineralized hard component,which exhibits brittle fracture, and a softer organic component, which is primarily chitin.These two components are shown in the Fig. 5. The brittle component is arranged in ahelical pattern called Bouligand structure [46,47]. Each of these mineral ‘rods’ (!1 lmdiameter) contains chitin–protein fibrils with approximately 60 nm diameter. These, ontheir turn, are comprised of 3 nm diameter segments. There are canals linking the insideto the outside of the shell; they are bound by tubules (0.5–1 lm) shown in the micrographand in schematic fashion. The cross-section of hard mineralized component has darkerspots seen in the SEM.

Fig. 5. Hierarchy of crab exoskeleton.


3. Multifunctionality and self-healing

Most biological materials are multifunctional [4], i.e., they accumulate functions such as

(a) Bone: structural support for body plus blood cell formation.(b) Chitin-based exoskeleton in arthropods: attachment for muscles, environmental pro-

tection, water barrier.(c) Sea spicules: light transmission plus structural.(d) Tree trunks and roots: structural support and anchoring plus nutrient transport.(e) Mammalian skin: temperature regulation plus environmental protection.(f) Insect antennas: they are mechanically strong and can self-repair. They also detect

chemical and thermal information from the environment. They can change theirshape and orientation.

Another defining characteristic of biological systems, in contrast with current syntheticsystems, is their self-healing ability. This is nearly universal in nature. Most structures canrepair themselves, after undergoing trauma or injury. Exceptions are teeth and cartilage,that do not possess any significant vascularity. It is also true that brains cannot self-repair;however, other parts of the brain take up the lost functions.

4. Self-organization and self-assembly

In the traditional study of thermodynamics, we, Materials Scientists, restrict ourselves,for the most part, to isolated and closed systems. We know, from the second law of ther-modynamics, that in an isolated system equilibrium is reached at maximum entropy. If t isdefined as time, a system will approach equilibrium as

dS=dt > 0 "1#

Thus, we learn that the entire universe marches inexorably toward entropy maximiza-tion. This translates into disorder because disordered states have a greater number of pos-sible configurations, W (recall that S = k lnW).

For closed systems, equilibrium is reached when the free energy is minimized. If pres-sure and temperature are constant, the Gibbs free energy is used; for systems at constantvolume and temperature, the Helmholtz free energy criterion holds. However, we knowthat temporal evolution in nature starts from simpler to more complex structures andleads to ever greater order and self-organization. This is clear around us: subatomic par-ticles aggregate to form atoms, atoms combine to form compounds, organic compoundsform complex molecules which eventually lead to life, life progresses from the simplestto the more complex forms, biological units combine in ever increasing complex arrays,civilizations form and evolve. How can all this be reconciled with thermodynamics? Theseminal work of Prigogine [48,49], 1977 Nobel Laureate in Chemistry, is essential toour understanding. He developed the thermodynamics of irreversible systems and pro-vided a link between thermodynamics and evolution. This was actually preceded by Teil-hard de Chardin, a French paleontologist and philosopher that advanced the law ofcomplexity-conscience. In his classic work, ‘Le Phenomene Humain’ [50], he proposedboldly that complexity inexorably increases in the universe at the expense of a quantity


which he named ‘physical energy.’ This increase in complexity results in an increase inconscience.

Most complex systems are indeed open and o! equilibrium. Prigogine demonstratedthat non-isolated (open) systems can evolve, by self-organization and self-assembly,toward greater order [48,49]. Open systems exhibit fluxes of energy, matter, and exchangesin mechanical, electrical, and magnetic energy with the environment. The entropy varia-tion can be expressed as having two components: one internal, i, and one due to theexchanges, e:

dS=dt $ diS=dt % deS=dt "2#

If the system were isolated, we would have deS/dt = 0. For an open system, this term isnot necessarily zero. There is no law dictating the sign of deS/dt and it can be either posi-tive or negative. The second law still applies to the internal components, i. Thus

diS=dt > 0 "3#

Thus, it is possible to have a temporal decrease in S, if the flux component contributeswith a su"ciently negative deS/dt term: dS/dt < 0 if deS/dt > &di S/dt.

The physical interpretation of Eq. (2) is that order can increase with time. This is a sim-ple and incomplete explanation for the origin of complex phenomena. Irreversible thermo-dynamics of complex systems involves other concepts such as perturbation and symmetrybreaking. Nicholas and Progogine [49] showed that non-linearities combined with non-equilibrium constraints can generate multiple solutions through bifurcation and thus allowfor more complex behavior in a system. The biosphere is an example of an open system,since it receives radiative energy from the sun and exchanges energy with the earth.

Self-organization is a strategy by which biological systems construct their structures.There are current e!orts at this design strategy duplicating in order to manufacture syn-thetic structures. Among the first were Nuzzo and Allara [51] who fabricated self-assem-bled monolayers (SAMs). This work and other work by Whitesides [37,52] and Sarikaya[53] (GEPIs) will be reviewed in Section 11. (Biomimetics) is laying the groundwork forbiologically inspired self-assembly processes which have considerable technologicalpotential.

As an example of a self-assembled structure, Fig. 6a shows a schematic rendition of adiatom. The end surface is shown in Fig. 6b. This elaborate architecture is developed byself-assembly of the enzymes forming a sca!old upon which biomineralization takes place[54,55]. These orifices are each at the intersections of three lines: two spiral lines withopposite chirality and radiating lines. The rows of orifices radiating from the center exhibit‘dislocations’ since the number of spokes has to increase with the radius. These disloca-tions are marked with circles in Fig. 6c. The orifices have a striking regularity and spacing,as shown in Fig. 7. Their diameter is approximately 2 lm and they each have a ridge thatserves, most probably, as reinforcement, such as in cast iron components.

5. Basic building blocks (nano and microstructure of biological materials)

Biological materials are more complex than synthetic materials. As seen in the previoussections, they form complex arrays, hierarchical structures and are often multifunctional,i.e., one material has more than one function. We classify biological materials, from themechanical property viewpoint, into soft and hard. Hard materials provide the skeleton,


teeth, and nails in vertebrates and the exoskeleton in arthropods. Soft biological materialsbuild skin, muscle, internal organs, etc. Table 3 provides the distribution (on a weight per-centage) of di!erent constituents of the human body.

Here are some examples of ‘‘hard’’ biological materials:

Calcium phosphate (hydroxyapatite-Ca10(PO4)6(OH)2): teeth, bone, antlers.Calcium carbonate (aragonite): mollusk shells, some reptile eggs.

(calcite): bird eggs, crustaceans, mollusks.Amorphous silica (SiO2(H2O)n): spicules in sponges, diatoms.Iron oxide (Magnetite-Fe3O4): teeth in chitons (a weird looking marine worm), bacteria.Collagen: organic component of bone and dentine, tendons, muscle, blood vessels.

Fig. 6. (a) A cylindrical silica diatom; (b) end surface of cylindrical silica diatom showing self-organized patternof orifices. Notice spiral patterns (both chiralities); (c) center of cylinder with radiating spokes; extremities of‘dislocations’ marked by circles (courtesy of E. York, Scripps Institute of Oceanography, UC San Diego).


Chitin: arthropod and insect exoskeletons.Cellulose: plant cell walls.Keratin: bird beaks, horn, hair.Elastin: skin, lungs, artery walls.

Of the above, iron oxide, carbon phosphate, calcium carbonate, silica, and iron oxideare minerals. Chitin and cellulose are polysaccharides. Collagen, keratin and elastin areproteins (polypeptides).

5.1. Molecular units

In order to fully understand proteins, we have to start at the atomic/molecular level, aswe did for polymers. Actually, proteins can be conceived of as polymers with a greaterlevel of complexity. We start with amino acids, which are compounds containing bothan amine (–NH2) and a carboxyl (–COOH) group. Most of them have the structure:

H

R C COOH

NH2

Fig. 7. Detailed view of orifice; back surface of diatom with hexagonal pattern can be seen in central orifice(Courtesy of E. York, Scripps Institute of Oceanography, UC San Diego).

Table 3Occurrences of di!erent biological materials in body

Biological material Weight percentage in human body

Proteins 17Lipids 15Carbohydrates 1Minerals 7DNA, RNA 2Water 58


Table 4Eight of the 20 amino acids found in proteins

Name Chemical formula

Alanine (Ala)

Leucine (Leu)

Phenylalanine (Phe)

Proline (Pro)

Serine (Ser)

Cysteine (Cys)

Glutamate (Glu)

(continued on next page)


R stands for a radical. Table 4 shows eight main amino acids. There are 20 di!erentamino acids in proteins. In addition to these eight, we have the following: Arginine(Arg), Asparagine (Asn), Aspartate (Asp), Glutamine (Gln), Glycine (Gly), Histidine(His), Isoleucine (Ile), Methionine (Met), Threonine (Thr), Tryptophan (Trp), Tyrosine(Tyr), and Valine (Val).

Deoxyribonucleic (DNA) and ribonucleic acid (RNA) are the molecular repositories ofgenetic information. The structure of protein is a product of information programmedinto the nucleotide sequence of a nucleic acid. Nucleotides are the building blocks ofnucleic acids. In DNA, the four nucleotides present are designated by the letters ACTG:Adenine, Cytosine, Thymine, and Guanine. A links to T and G links to C trough hydro-gen-bonding, as shown in Fig. 8.

The amino acids form linear chains similar to polymer chains; these are called polypep-tide chains. These polypeptide chains acquire special configurations because of the forma-tion of bonds (hydrogen, van der Waals, and covalent bonds) between amino acids on thesame or di!erent chains. The two most common configurations are the alpha helix and thebeta sheet. Fig. 9 shows how an alpha helix is formed. The NH and CO groups formhydrogen bonds between them in a regular pattern, and this creates the particular confor-mation of the chain that is of helical shape. The backbone of the chain is shown as darkrods and is comprised of a repeating segment of two carbon and one nitrogen atoms. In

Table 4 (continued)

Name Chemical formula

Lysine (Lys)

Fig. 8. Arrangement of four nucleosides (Adenine, Cytosine, Thymine, Guanine) and the hydrogen-bonding (Ato T, C to G) across chain in DNA.


Fig. 9. (a) Structure of alpha helix; dotted double lines indicate hydrogen bonds; (b) structure of beta sheet withtwo anti-parallel polypeptide chains connected by hydrogen bonds (double dotted lines) (from Lodish et al. [56]).

Fig. 10. (a) Hydrogen bond connecting a CO to a NH group in a polypeptide; (b) successive hydrogen bonds onsame polypeptide chain leading to formation of a helical arrangement (From Human Physiology 8th edition byVander et al. [57, Fig. 2.18, p. 29]).


Fig. 9b several hydrogen bonds are shown, causing the polypeptide chain to fold. The rad-icals stick out. Another common conformation of polypeptide chains is the beta sheet. Inthis conformation, separate chains are bonded. Fig. 9 shows two anti-parallel chains thatare connected by hydrogen bonds (shown, again, by double dashed lines). We can see thatthe radicals (large grey balls) of two adjacent chains stick out of the sheet plane on oppo-site sides. Successive chains can bond in such a fashion, creating pleated sheets. Fig. 10shows the hydrogen bond and the a helix in greater detail. It is the hydrogen bonds thatgive the helical conformation to the chain, as well as the connection between the adjacentchains in the b sheet. This is shown in a clear fashion in Fig. 10a. The hydrogen bonds areindicated by double dashed lines.

The three main fiber-forming polymers in the nature are

• Polypeptide chains, which are the building blocks for collagen, elastin, silks, andkeratins.

• Polysaccharides, the building blocks for cellulose and hemicellulose.• Hybrid polypeptide–polysaccharide chains, the building blocks for chitin.

Polysaccharides will be discussed in Section 5.4.

5.2. Biominerals

One of the defining features of the rigid biological systems that comprise a significantfraction of the structural biological materials is the existence of two components: a mineral

Fig. 11. (a) Atomic structure of hydroxyapatite; smallest white atoms: P; largest gray atoms: O; medium blackatoms: Ca (b) atomic structure of aragonite; large dark atoms: Ca; small gray atoms: C; large white atoms: O.


Table 5Principal components of common structural biological composites

Biologicalcomposite

Mineral Organic

Calciumcarbonate

Calciumphosphate

Silica Hydroxyapatite Other Keratin Collagen Chitin Cellulose Other

Shells X XHorns X XBones X XTeeth X XBird Beaks X XCrustacean

ExoskeletonX X X

Insect Cuticle X XWoods XSpicules X X

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and an organic component. The intercalation of these components occurs at the nano,micro, or mesoscale and often takes place at more than one-dimensional scale. Table 5exemplifies this, for a number of systems. The mineral component provides the strengthwhereas the organic component contributes to the ductility. This combination of strengthand ductility leads to high energy absorption prior to failure. The most common mineralcomponents are calcium carbonate, calcium phosphate (hydroxyapatite), and amorphoussilica, although over 20 minerals (with principal elements being Ca, Mg, Si, Fe, Mn, P, S,C, and the light elements H and O) have been identified. These minerals are embedded incomplex assemblages of organic macromolecules which are on their turn, hierarchicallyorganized. The best known are keratin, collagen, and chitin.

Table 6 shows the minerals that have been identified in biological systems [58]. Thenumber of minerals is continuously increasing.

Table 6Principal minerals found in biological systems (from Weiner and Addadi [58])

Carbonates Calcite Amorphous calcium carbonate familyAragonite HydrocerrusoteVaterite ProtodolomiteMonohydrocalcite

Phosphates Carbonated apatite (dahllite) BrushiteFrancolite Amorphous calcium phosphate familyOctacalcium phosphate VivianiteWhitlockite Amorphous pyrophosphateStruvite

Halides Fluorite Amorphous fluoriteHieratite Atacamite

Sulfates Gypsum JarositeCelestite Calcium sulfate hemihydrateBarite

Silicates Silica (opal)

Oxides and hydroxides Magnetite Amorphous manganese oxideGoethite Amorphous ilmeniteLepidocrocite TodotokiteFerrihydrite BirnessiteAmorphous iron oxide

Sulfides Pyrite GalenaAmorphous pyrrhotite GreigiteHydrotroilite MackinawiteShalerite Wurtzite

Native element Sulfur

‘‘Organic Minerals’’ Whewellite Uric acidWeddelite Para"n hydrocarbonManganese oxalate WaxCalcium tartrate Magnesium oxalate (glushinskite)Calcium malate Copper oxalate (moolooite)Earlandite Ferric oxalate anhydrousGuanine Sodium urate


Fig. 11a shows the atomic arrangement of the calcium, phosphorus, and oxygen atomsin hydroxyapatite. The unit cell is quite complex and consists of four primitive hexagonalcells juxtaposed (top view). We should remember that the hexagonal cell is composed ofthree primitive cells, brought together at their 1200 angles (3 · 120" = 360"). In the caseof the hydroxyapatite unit cell, there are four unit cells: two at the 60" angle and two atthe 120" (2 · 60" + 2 · 120" = 360").

Fig. 11b shows the aragonitic form of calcium carbonate. Aragonite has the ortho-rhombic structure. However, it is important to recognize that the minerals do not occurin isolation in living organisms. They are invariably intimately connected with organicmaterials, forming complex hierarchically structured composites. The resulting compositehas mechanical properties that far surpass those of the monolithic minerals. Although wethink of bone as a cellular mineral, it is actually composed of 60% collagen and 30–40%hydroxyapatite (on a volume basis). If the mineral is dissolved away, the entire collagenframework is retained.

5.2.1. BiomineralizationOrganic molecules in solution can influence the morphology and orientation of inor-

ganic crystals if there is molecular complementarity at the crystal-additive interface. Phasetransformations are believed to occur by surface dissolution of precursors which mediatethe free energies of activation of interconversions. Yet these principles are yet to be welldeveloped. Understanding the process in which living organisms control the growth andstructure of inorganic materials could lead to significant advances in Materials Science,opening the door to novel synthesis techniques for nano scale composites. Mann [31] statesthat in order to address the question of nanoscale biologically-induced phase transforma-tions and crystallographic control we must study the bonding and reactivity of extendedorganized structures under the mediation of organic chemistry. We examine two impor-tant processes: nucleation and morphology.

5.2.2. NucleationThe control of nucleation of inorganic materials in nature is achieved by the e!ect of

activation energy dependency on organic substrate composition. Inorganic precipitationis controlled by the kinetic constraints of nucleation. Mann [31] states that this activationenergy may also depend on the two-dimensional structure of di!erent crystal faces, indi-cating that there is a variation in complementarity of various crystal faces and the organicsubstrate. Weissbuch et al. [59] describe the auxiliary molecules which promote or inhibitcrystal nucleation depending on their composition.

5.2.3. MorphologyThe morphology of the inorganic material created in nucleation is controlled through

the interaction with the organic matrix. Activation energies can be influenced in the pres-ence of an organic matrix in three possible ways. Fig. 12 describes the possibilities of poly-morphic nucleation [31]. The activation energies of two non-specific polymorphs, ‘‘A’’ and‘‘B’’, are shown in the presence (state 2) and absence (state 1) of the organic matrix. If ‘‘A’’is more kinetically favored in the absence of the organic matrix then it is possible to exam-ine the possibilities of organic e!ect on the activation free energy (DG#) of various poly-morphs with respect to each other. In the first case both polymorphs are a!ected equally,


thus ‘‘A’’ remains kinetically favorable. In the second case the e!ect on the ‘‘B’’ poly-morph is much larger than for ‘‘A’’ and thus, when in the presence of the organic matrix,

Fig. 12. Structural control by organic matrix-mediated nucleation. (a) Promotion of non-specific nucleation inwhich both polymorphs have the activation energies reduced by the same amount; (b) promotion of structure-specific nucleation of polymorph B due to more favorable crystallographic recognition at the matrix surface; (c)promotion of a sequence of structurally non-specific to highly specific nucleation (from Mann [7, p. 110,Fig. 6.29]).

Fig. 13. Representation of activation energies of nucleation in the presence and absence of an organic matrix fortwo non-specific polymorphs (from Mann [7, p. 60, Fig. 4.25]).


‘‘B’’ is kinetically favorable. In the last case we see a combination of the two earlier cases,in which the kinetic favorability of the two polymorphs is influenced by genetic, metabolic,and environmental processes.

The selection of the polymorph will also be determined by the transformation sequence.This starts, in Fig. 13, with an amorphous mineral and continues through a series of inter-mediate structures that have the same composition but decreasing free energy (increasingthermodynamic stability [31,60]). This cascade is shown in Fig. 13. The system will eitherfollow the one step route (A) or travel along a sequential transformation route (B) depend-ing on the activation energies of nucleation, growth, and transformation. Addadi et al.[61–63] proposed that the role of the solid-state amorphous precursor phase could be fun-damental in the biomineralization process.

The composition of the complex structure in nacre and other biocomposites is mediatedby the phase transformations which occur by surface dissolution of the precursor. Thephase transformation is dictated by the solubility of amorphous precursor into the crystal-line intermediates, and the e!ect of these precursors on the free energies of activation ofthese interconversions. Thus an animal which is able to control its emission of molecularprecursor (organic matrix, or soluble protein) will be able to control the growth and struc-ture of its inorganic biocomposite. Addadi and Weiner [61] and Addadi et al. [62,63] dem-onstrated the stereoselective adsorption of proteins in the growth of calcite crystalsresulting in a slowing down of growth in the c direction and altering the final shape ofthe crystal. This evidence of the influence of organics on inorganic crystal growth led themto examine the influence of proteins on the morphology of crystal growth.

Belcher et al. [64] showed that a controlled phase transition between aragonite and cal-cite in nacre could be obtained in the laboratory with the use of soluble polyanionic pro-teins. They showed that biological phase transformation did not require the deposition ofan intervening protein sheet, but simply the presence of soluble proteins. This was directlyobserved by Hansma et al. [65] through atomic force microscopy. Mann et al. [60]explained the role of soluble proteins as e!ective agents to the reduction of interfacial ener-gies on the surface of the inorganic. An increase in hydrophobicity of the additive reducesits ability to control morphology and phase transition during crystallization. The e!ective-ness of the soluble proteins in the process of morphology control depends on their inter-action with crystal surfaces in a way which is identical to that of an organic matrix (proteinsheet). Thus, the e!ect of the protein sheet is the control of crystal orientation with respectto bonding energies of specific crystal phases.

Fig. 14. AFM images showing; (a) pure calcite growth hillock. (b–d) Growth hillocks after the addition ofsupersaturated solutions of (b) glycine, an achiral amino acid, (c and d) aspartic acid enantiomers (from Ormeet al. [66, p. 776, Fig. 1]).


Orme et al. [66,67] reported a dependency of calcite growth morphology on the selectivebinding of amino acids on the crystal step-edges. Through in situ atomic force microscopythey were able to show that in solution amino acids bind to geometric and chemicallyfavored step-edges, changing the free energy of the step-edge. Fig. 14a shows the AFMimage of pure calcite growth hillocks. When a supersaturated solution of glycine is intro-duced into the growth solution, it can be observed in Fig. 14b that the two acute stepsbecome curved. By modifying the free energy of step-edges, preferential attachment of cal-cium ions onto specific locations can be controlled, thus resulting in macroscopic crystalshape manipulation. Similar results were obtained following the addition of aspartic acidenantiomers, Fig. 14c and d. The importance of this observation is the verification of suchtheories as those proposed by Mann et al. [60], proving that the addition of variousorganic growth modifiers can change the rate and location in which calcite attaches ontosurfaces. In essence, this is an in situ observation of nature’s hand laying the bricks of self-organization and biomineralization.

5.3. Proteins (polypeptides)

The principal organic building blocks in living organisms are the proteins. The wordcomes from Greek (Proteios) which means ‘‘of first rank’’ and indeed proteins play akey role in most physiological processes. The soft tissues in the mammalian body are madeof proteins. They are also an important component of biominerals.

5.3.1. CollagenCollagen is a rather sti! and hard protein. It is a basic structural material for soft and

hard bodies. It is present in di!erent organs and tissues and provides structural integrity.Fung [24] compares it to steel in structures, not because of its strength, but because it is abasic structural component in our body. Steel is the principal load carrying component instructures. In living organisms, collagen plays the same role: it is the main load carryingcomponent of blood vessels, tendons, bone, muscle, etc. In rats, 20% of the proteins arecollagen. Humans are similar to rats in physiology and behavior, and the same proportionshould apply. Approximately 20 types of amino acid compositions of collagen have beenidentified and their number is continuously increasing. In humans (and rats) the collagen isthe same, called Type I collagen. Other collagens are named II, X, etc. The amino acidcomposition of di!erent collagens di!ers slightly. This composition gives rise to the di!er-ent types. Table 7 [68] provides a few illustrative examples.

Fig. 15 shows the structure of collagen. It is a triple helix, each strand being made up ofsequences of amino acids. Each strand is itself a left-handed a helix with approximately0.87 nm per turn. The triple helix has a right-handed twist with a period of 8.6 nm. Thedots shown in a strand in Fig. 15 represent glycine and di!erent amino acids. Fiber form-ing collagens organize themselves into fibrils. Fig. 16 is a transmission electron micrographof tendon fibrils [69]. Each fibril has transverse striations, which are spaced approximately67 nm apart. These striations are due to the staggering of the individual collagen mole-cules. The length of each collagen molecule is approximately 300 nm, which is about 4.4times the distance of stagger, 67 nm. The gap between adjacent chains is about 35 nm(67 · 5 & 300 = 35) and the overlap is about 32 nm (300 & 67 · 4 = 32). Thus, there is aperiodicity in the structure, shown on the right hand side in Fig. 17b. Each repeating unitis comprised of five segments and this periodicity produces a characteristic interference


Table 7Amino acid composition from several collagens (Adapted from Ehrlich and Worch [68])

Collagen sources Amino acid (%)

Asp Thr Ser Glx Pro HyPr Gly Ala Val Met Ile Leu Tyr Phe His HyLys Lys Arg

Sturgeon swim-bladder 6.9 3.8 5.8 11.4 12.8 11.8 27.7 11.6 2.3 1.4 1.7 2.6 0.5 2.5 0.8 1.9 3.5 10.0Shark 6.4 2.4 3.3 11.0 13.3 8.8 25.4 11.4 2.7 1.8 2.7 2.6 7.2 2.1 1.7 0.9 3.7 8.6Femur of ox 4.3 1.9 3.5 6.5 11.8 10.3 31.7 10.8 2.4 0.5 1.3 3.0 0.7 1.9 0.6 0.8 3.0 5.0Porcine skin 5.1 1.7 3.5 11.4 13.3 12.6 22.1 8.7 2.1 0.5 1.1 2.9 0.5 1.9 0.7 – 3.5 8.4Human tendon 3.9 1.5 3.0 9.5 10.3 7.5 26.4 9.0 2.1 0.5 0.9 2.1 0.3 1.2 1.4 1.5 3.5 16.0Human bone 3.8 1.5 2.9 9.0 10.1 8.2 26.2 9.3 1.9 0.4 1.1 2.1 0.4 1.2 1.4 0.6 4.6 15.4

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pattern that is observed as bands in electron microscopy, and is shown in Fig. 17c. Thecollagen chains are directional, i.e., they have a ‘‘head’’ and a ‘‘tail’’, and the staggeredarrangement allows for bonding between the ‘‘head’’ of one chain and the ‘‘tail’’ of theadjacent one, as shown in Fig. 17b.

The collagen molecules, with a diameter of !1.5 nm, form fibrils with diameter of!50 nm. The molecules attach to the adjacent molecules by intrafibrillar bonding. Thesefibrils form fibers, with diameter of !1 lm. This is mediated by proteoglycans. Microfi-brils, in turn, arrange themselves into fibrils, which are organized into fibers. Fibers arebundles of fibrils with diameters between 0.2 and 12 lm. In tendon, these fibers can beas long as the entire tendon. In tendons and ligaments, the collagen fibers form primarilyone-dimensional networks. In skin, blood vessels, intestinal mucosa and the female vaginaltract, the fibers organize themselves into more complex patterns leading to two- and three-dimensional networks.

Fig. 15. Triple helix structure of collagen (adapted from Fung [24, p. 248, Fig. 7.3.1]).

Fig. 16. Transmission electron micrograph of tendon fibrils (from Traub et al. [69, p. 9819, Fig. 4]).


Fig. 17. Collagen-composed triple helix, forming microfibrils which have 67 nm gaps; (a) general scheme; (b)representation of 300 nm segments with gaps and overlaps (c) electron micrograph (from Lodish et al. [56,Fig. 22-11]).


Fig. 18 [70] shows the hierarchical organization of a tendon, starting with tropocollagen(a form of collagen), and moving up, in length scale, to fascicles. There is a crimped orwavy structure shown in the fascicles that has an important bearing on the mechanicalproperties. Fig. 19 shows an idealized representation of a wavy fiber. Two parametersdefine it: the wavelength 2l0 and the angle h0. Typical values for the Achilles tendon ofa mature human are l0 = 20–50 lm and h0 = 6–8". These bent collagen fibers stretch outin tension. When the load is removed, the waviness returns. When the tendon is stretchedbeyond the straightening of the waviness, damage starts to occur. Fig. 20a shows a sche-matic stress–strain curve for tendon. The tendon was stretched until rupture. There areessentially three stages:

Fig. 18. Hierarchical structure of tendon starting with collagen molecules and techniques used to identify it (fromBaer et al. [70, p. 60]).

Fig. 19. Idealized configuration of a wavy collagen fiber.


Region I: toe part, in which the slope rises rapidly. This is the physiological range inwhich the tendon operates under normal conditions.

Region II: linear part, with a constant slope.Region III: slope decreases with strain and leads to failure.

The elastic modulus of collagen is approximately 1–1.5 GPa and the maximum strain isin the 10–20% range. The maximum strength is approximately 70–150 MPa. Cross-linkingincreases with age, and collagen becomes less flexible. Collagen often exists in combinationwith other proteins. An example is the ventricular papillary muscle. Fig. 20b shows thestress–strain curve. The passive tension in the cardiac muscle is governed by two-loadbearing elements in the heart, collagen and titin. Titin has a spring-like region withinthe I-band of the sarcomere units (seen Section 5.3.3). As the sarcomere units areextended, passive tension increases. At lower strains titin determines most of the passivetension in the heart. At higher strains, collagen begins to straighten and align with the axis

Fig. 20. (a) Stress–strain curve of collagen with three characteristic stages; I: Toe; II: linear elastic; III: failure. (b)Stress–strain curve for ventricular papillary muscle, composed of titin and collagen (courtesy of A. Jukiel, Dept.of Bioengineering, UCSD [99]).


of force and hence it contributes increasingly to the passive tension. Fig. 20b shows thecharacteristic toe region followed by a linear response.

It is possible to determine the maximum strain that the collagen fibers can experiencewithout damage if their shape is as given in Fig. 19 with a ratio between amplitude andwavelength of r. We can assume a sine function of the form:

y $ k sin 2px=k "4#

The maximum of y is reached when x = k/4.The relationship between h0, l0, and the amplitude of the sine function is:

dydx

$ 2kpk

cos2pxk

"5#

For x = 0

tan h0 $dydx

!!!!x$0

$ 2kpk

"6#

Hence

ymax $l0ptan h0 "7#

We can integrate over the length of the sine wave from 0 to 2p. However, this will lead toan elliptical integral of di"cult solution. A simple approximation is to consider the shapeof the wavy protein as an ellipse with major axis 2a and minor axis 2b. The circumferenceis given by the approximate expression:

L ' p3

2"a% b# & "ab#1=2

" #"8#

In the sine function, we have two arms, one positive and one negative. Their sum corre-sponds, in an approximate manner, to the circumference of the ellipse.

The strain is equal to

e $ L& 4a4a

$p 3

2 "a% b# & "ab#1=2h i

& 4a

4a"9#

Thus

e $ p4

3

21% b

a

$ %& b

a

$ %1=2" #

& 1 "10#

The following ratio is defined: ba $ 2r.

The corresponding strain is

e $ p4

3

2"1% 2r# & "2r#1=2

" #& 1 "11#

Beyond this strain, the collagen will undergo bond stretching and eventually break.The mechanical properties of collagen connective tissue are dictated, to a large extent,

by the structure of the constituent collagen, which can form networks that are one-, two-,or three-dimensional. In the case of planar soft tissues, the deformation is complex. An


example of this is the pericardium, which is a double-walled sac that contains the heart. Ithas a crimped collagen structure shown in Fig. 21a. The crimp period of !30 lm and theamplitude of !15 lm were estimated by Liao et al. [71]. Synchroton small angle X-rayscattering (SAXS) was used to follow the molecular D spacing (the 67 nm periodicity)of the collagen as a function of imposed stretching. The results are shown in Fig. 21b.Using Eq. (11) one can estimate the total nominal strain required to completely uncrimpand straighten the collagen structure shown in Fig. 21a. The ratio 2r is

2r $ ba$ 15

30$ 0:5 "12#

The corresponding maximum nominal strain is

e $ 0:22

This is slightly higher than the strain at which molecular bond stretching is initiatedin Fig. 21b. Up to 0.2, the strains in the fibrils are negligible. Beyond this strain, themolecules stretch. However, not all external strain is accommodated by molecular bond

Fig. 21. (a) Crimped collagen structure in bovine pericardium crimp period !30 lm and amplitude !15 lm; (b)molecular strain (as determined from change in D period) as a function of externally applied extension for bovinepericardium collagen (from Liao et al. [71, Figs. 9 and 4(a), pp. 51, 49]).


stretching (the increase from 67 nm). Otherwise, the slope in the second stage would beequal to 1. One can speculate that part of the strain is accommodated by residual uncrim-ping of the structure (the last 0.02) and part by interfibril shear.

Another example illustrating the power of synchrotron X-ray scattering are the resultsby Fratzl et al. [72] on rat tail tendon. They are shown in Fig. 22. The mechanical tensileforce is also plotted. The toe and linear portions of the collagen response are clearly seen.In the bottom portion of the figure, the change in length in the molecular repeat length isshown. The D repeat unit length is constant until a strain of 0.05. This indicates that therat tendon is sti!er than the bovine pericardium. This is consistent with the parameters inthe sine function reported by Fung [25] for the rat tail tendon:

l0 $ 100 lm

h0 $ 12(

The corresponding parameters in Eq. (10) are a = 100 lm and b = 6.75 lm. The maximumnominal strain calculated from Eq. (11) is 0.13. In Fig. 22, the molecular stretching ofbonds starts for a strain of 0.05. The slope of the linear portion of the curve is equal to0.4, indicating that one has concomitant molecular bond stretching, uncrimping of thestructure, and possibly shear between fibrils or fibers beyond this point. These results cor-roborate the bovine pericardium results in Fig. 21b.

Fig. 22. Top: tension; and bottom: molecular strain (as determined from change in D period) as a function ofexternally applied extension for rat tail collagen (from Fratzl et al. [72, Fig. 3, p. 122]).


The stress–strain response of collagen can be represented mathematically and indeedFung [24] proposed the following expression for the toe region:

r $ C eak & ea& '

$ C eae & 1" # "13#

where C and a are parameters and k is the stretch ratio (=e + 1). This equation was alsoused by Sacks [73]. Another expression is the Mooney–Rivlin [74,75] equation for rubbers,both the toe and linear regions can be described by

r $ C1 1% l1

k

$ %k2 % 1

k

$ %1

k"14#

where the parameter l has one value for the toe region and is equal to zero in the linearregion. Collagen is also viscoelastic and therefore a relaxation function has to be added tothe constitutive description.

5.3.2. KeratinKeratin is a structural protein that is found in most vertebrate animals. It is a fibrous

protein that is produced in the integument (outer covering) of organisms and is typified bysulfur content. The integument provides the protective layer of animals and consists of twostructural entities: the dermis and epidermis. The dermis lies underneath the epidermis andis made of mainly elastin and collagen. The epidermis is the outer layer, produced by thedermis, and is made from epidermal cells. Keratin is produced by the keratinization pro-cess where epidermal cells die and build up at the outermost layer. It is usually classified assoft and hard originating from di!erent mechanisms of biosynthesis. It is further classifiedinto a- and b-keratin, depending on its molecular structure. a-keratin, commonly knownas mammalian keratin, is found in skin, wool, hoof, whale baleen; b-keratin, also known

Fig. 23. (a) One of the pair of symmetry-related strands of b-sheets that make up the central framework of thefilament. (b) Model for the arrangement of the b-sheet portions of the protein molecules in the filaments of aviankeratin (from Fraser and Parry [77, p. 208, Fig. 1]).


as avian and reptilian keratin, is found in claw, scale, feather, and beaks [18,76]. The shellof the toucan beak presented in Section 9.2 is made of b-keratin. A major di!erencebetween a-keratin and b-keratin is intermediate filament (IF). The IF of the a-keratinstructure is based on a-helix folding pattern. This is a coiled structure similar to collagen(three interwoven helices). These helices combine themselves to form microfibrils with adiameter of 8 nm. Fig. 23 shows the microfibril of b-sheet. The folding pattern of b-keratinis b-sheet [77] and the diameter of b-keratin is 4 nm. The IF of b-keratin has a smallerdiameter and the filament has a helical structure with a pitch of 9.5 nm and four turns

Fig. 24. Molecular structure of (a) actin and (b) myosin; (c) action of cross-bridges when actin filament is movedto left with respect to myosin filament; notice how cross-bridges detach themselves, then reattach themselves toactin.


per unit [77]. Interestingly, it undergoes a phase transformation (a–b transition) under ten-sile load, which increases its elongation [78].

Keratin is considered as a biological fiber-reinforced composite consisting of a highmodulus fiber and a lower modulus viscoelastic matrix. The matrix plays a role as a med-ium to transfer the applied load to the fiber, thus preventing crack propagation from localimperfections or points of rupture [79]. Mineralization with calcium and other salts con-tributes to the hardness of keratin [80]. In mammalian keratin, the a-helix is alignedalmost parallel to the filament. a-keratin is mechanically linear elastic. While b-keratinis quite di!erent from a-keratin in molecular structure, the b-sheet also behaves linearlyelastically and the mechanical behavior is similar. a-keratin changes the structure intothe b-keratin during stretching [78]. This change can be observed through X-ray di!rac-tion. Generally, the sti!ness of the b-sheet is higher than that of the a-helix. The mechan-ical behavior of both a-keratin and b-keratin depends on moisture content. Increasinghydration content decreases the sti!ness and modulus [77] because the matrix of keratinabsorbs moisture. The mechanical properties of keratinous materials and bird feather willbe presented in Sections 7.4 and 9.4, respectively.

Fig. 25. Structure of muscle, from the (a) sarcomere units, to (b) myofibril, and finally to (c) fibers.


5.3.3. Actin and myosinThese are the principal proteins of muscles, leukocytes, and endothelial cells. Muscles

contract and stretch through the controlled gliding/grabbing of the myosin with respectto the actin fibers. Fig. 24a shows an actin fiber. It is composed of two polypeptides ina helical arrangement. Fig. 24b shows the myosin protein. It has little heart-shaped ‘‘grap-plers’’ called cross-bridges. The tips of the cross-bridges bind and unbind to the actin fil-aments. Fig. 24c shows the myosin and actin filaments, and the cross-bridges at di!erentpositions. The cross-bridges are hinged to the myosin and can attach themselves to di!er-ent positions along the actin filaments, as the actin is displaced to the left. Thus, the mus-cles operate by a micro-telescoping action of these two proteins. They form sarcomereunits which are actin–myosin arrays in the pattern shown in Fig. 25a.

Fig. 25 shows how the filaments organize themselves into myofibrils. Bundles of myo-fibrils form a muscle fiber. The Z line represents the periodicity in the myosin–actin units(that are called sarcomeres) and is approximately equal to 3 lm in the stretched configu-ration (Fig. 25b). It shortens when the muscle is contracted. This gives the muscle a stri-ated pattern when observed at high magnification. They resemble a coral snake in themicroscope. Myofibrils have a diameter of approximately 1–2 lm (Fig. 25b). They arrangethemselves in bundles with 20–100 lm in diameter, as shown in Fig. 25c.

5.3.4. ElastinElastin is one of the most stable and insoluble proteins in the body. The structure of

elastin is shown in Fig. 26 [81]. Each fibrous monomer is linked to many others and formsa three-dimensional network. Elastin is found in skin, walls of arteries and veins, and lungtissue. A prominent place is in the Ligamentum Nuchae, a long rope that runs along the top

Fig. 26. Molecular model for elastin (from Gray et al. [81, p. 465, Fig. 2]).


of the neck in horses and is constantly under tension. Other vertebrates have it too, but itis less pronounced. In this manner, similar to a cable in a crane, the horse can keep thehead up without using muscles. This Ligamentum Nuchae plays a role similar to the cablesin a suspension bridge. It is a rather robust cylinder, ideally suited for mechanical propertymeasurement. We will present the mechanical properties in Section 7.1.

5.3.5. Resilin and abductinResilin is found in arthropods. It has similar properties to elastin, but occurs in a total

di!erent animal and has a di!erent structure. When it is dry, it is hard, but can exhibit astrain of up to 3 before failure. This basic resilience is the source of its name. Its elasticmodulus in the range of stretch ratio (k) from 1 to 2 is approximately 1.8 MPa. Insectsuse resilin as elastic joints for their wings. Fleas and locusts use resilin at the base of theirhind legs as catapults in their jumping.

Abductin is the protein found in bivalve (scallop) hinges. Scallops use it to open thevalves. Abductin has about the same elastic modulus as resilin.

5.3.6. Other proteinsProteins are the most abundant biological macromolecules occurring in all cells. Thou-

sands of proteins of di!erent functionality can be found in a single cell. There is a greatvariety of proteins in biological systems that will not be covered here. Examples of rele-vance for us are lustrins [82], identified with abalone shell organic layer, and silicatein[83], found in sponge silica spicules.

Fig. 27. Chemical structures of chitin, chitosan, and cellulose (from Krajewska [88, Fig. 1]).


5.4. Polysaccharides

5.4.1. ChitinChitin is the second most abundant natural polymer (after cellulose) on earth. It is a

linear polysaccharide of b-(1-4)-2-acetamido-2-deoxy-D-glucose. The chemical structureof chitin is very similar to that of cellulose with a hydroxyl group replaced by an acetam-ido group. Pure chitin with 100% acetylation does not exist in nature. Chitin tends to forma co-polymer with its N-deacetylated derivative, chitosan. Chitosan is a polymer of b-(1-4)-2-amino-2-deoxy-D-glucose. The chemical structures of cellulose, chitin and chitosanare shown in Fig. 27 [84]. When the fraction of acetamido groups is more than 50% (morecommonly 70–90%), the co-polymer is termed chitin. The co-polymer consists of chitinand chitosan units randomly or block distributed through out the polymer chain, as shownin Fig. 28 [85].

Three polymorphic forms of chitin (a-, b-, and c-chitins) have been di!erentiated due totheir crystal structure as shown in Fig. 29. a-Chitin is arranged in an anti-parallel config-uration while b-chitin is organized in a parallel configuration. c-Chitin is a mixture ofa- and b-chitin. a-chitin is the most abundant form found in nature. The anti-parallel

Fig. 28. Chemical structural representation of chitin and chitosan co-polymer (from Kohr [84, p. 3, Fig. 1.2]).

Fig. 29. Three polymorphic configurations of chitin. (a) a-chitin (b) b-chitin (c) c-chitin.


configuration gives a-chitin a highly ordered crystalline structure with strong hydrogenbonding between chitin chains (Fig. 30). The strong hydrogen bonding leads to the rigidand insoluble properties of a-chitin. Both a-chitin and b-chitin are crystalline. The latticeparameter along the b-axis of a-chitin (1.886 nm) is approximately two times that ofb-chitin (0.926 nm); while that along the c-axis is approximately the same. This can be seenin the electron di!raction patterns (bc projection) shown in Fig. 31 [89].

Chitin is widely distributed in fungal and yeast cell walls, mollusk shells, arthropod exo-skeletons and other invertebrates. It plays an important role as the structural componentthat provides support and protection to the organisms.

The cell walls of fungi are made mostly of chitin. Fungal chitin forms randomly ori-ented microfibrils typically 10–25 nm in diameter and 2–3 lm long. Chitin microfibrilsare covalently linked to other polysaccharides, such as glucans, and form a chitin–glucancomplex which is the main structural component of fungal cell walls. The chitin content infungi varies from 0.45% in yeast to 10–40% in some filamentous fungi species.

The presence of chitin has been reported in shells of the mollusk species. Despite therelatively small amount of chitin compared to the inorganic mineral (typically CaCO3),

Fig. 30. The extensive hydrogen bonding between a-chitin chains (from Kohr [84, p. 74, Fig. 6.1]).


chitin plays an important role not only in the mechanical support but in the hierarchicalcontrol of the biomineralization processes. Studies on the organic matrix in the shell[87,88] revealed that the interlamellar sheets are composed of thin layers of b-chitin sand-wiched between two thick layers of silk-like protein gel. The b-chitin is highly ordered atthe molecular level and responsible for the overall shell formation. Weiss et al. [87] studiedthe distribution of chitin in shells of mollusk using chitin-binding green fluorescent proteinand confocal laser scanning microscopy. The results showed that bivalve mollusks depositand orient the chitin in a well defined manner. Chitin distributes mainly in the hinge andedges of the shell and integrates the flexible region connecting two valves.

Chitin is also the main component in the exoskeletons of arthropods. The exoskeletonmaterials of arthropods are complex composites that are hierarchically structured and mul-tifunctional, as shown in Fig. 5. The linear chitin chains align anti-parallel and form a-chi-tin crystals at the molecular level. Several of a-chitin crystals which are wrapped by proteinsform nanofibrils of about 2–5 nm in diameter and 300 nm in length. A bundle of chitin–pro-tein nanofibrils then form chitin–protein fibers of about 50–100 nm in diameter. These chi-tin–protein fibers align together forming planar layers which stack up helicoidally. Thisstructure is called a twisted plywood or Bouligand structure [46,47]. In crustaceans, suchas crabs and lobsters, there is a high degree of mineralization. The mineral is mostly calciumcarbonate, which deposits onto the space of chitin–protein network and gives rigidity to theexoskeleton. The multi-functionality and mechanical properties of arthropod exoskeletonsas well as the Bouligand structure are further discussed in Section 7.3.

5.4.2. CelluloseCellulose is the most abundant natural polymer, and is the structural component of

plant cell walls. It is a linear polysaccharide consisting D-anhydroglucopyranose units(often abbreviated as anhydroglucose units or as glucose units for convenience) linkedtogether by b-(1 ! 4)-glycosidic bonds, as shown in Fig. 32 [90].

Like amylase and amylopectin, the polysaccharides of starch, molecular cellulose is ahomopolysaccharide consisting of 10,000 to 15,000 D-glucose units. The main di!erencebetween cellulose and other D-glucose based polysaccharides is that the glucose residues

Fig. 31. Electron di!raction patterns of highly crystalline chitin: (a) a-chitin; (b) b-chitin (from Rinaudo [89, p.605, Fig. 3]).


in cellulose is in b configuration while that in amylase, amylopectin, and glycogen is in aconfiguration. This di!erence gives cellulose very unique physical and chemical properties.Most animals cannot digest cellulose, because they lack an enzyme to hydrolyze the b-(1 ! 4) linkages. Some animals, particularly ruminants and termites, can digest cellulosewith the help of a symbiotic microorganism which hydrolyzes the b-(1 ! 4) linkages.

For cellulose, the most stable conformation is that each unit chair is turned 180" rela-tive to its neighbors, yielding a straight, extended chain. When the cellulose is fullyextended, all hydroxyl groups are capable of forming both inter-molecular and intra-molecular hydrogen bonds (Fig. 32b). The extensive hydrogen bonds produce stablesupramolecular fibers with excellent mechanical properties. This property has made cellu-lose a useful material in civilization for millennia.

Cellulose forms a structure with regions of high order, i.e. crystalline regions, andregions of low order, i.e. amorphous regions. Naturally occurring cellulose (cellulose I)crystallizes in the monoclinic sphenodic structures. The unit cell of cellulose is shown inFig. 33 [91]; the lattice parameter are a = 0.835 nm; b = 1.03 nm; c = 0.79 nm.

Pure cellulose is never found in nature. The cotton fiber is the purest natural source,containing more than 95% of cellulose and about 5% of other substances. More com-monly, cellulose is associated with lignin and other substances so-called hemicellulosesin considerable quantities. The hemicelluloses are not forms of cellulose at all. Theycomprise a group of polysaccharides that remains associated with the cellulose after lignin

Fig. 32. The structure of cellulose. (a) Two units of a cellulose chain; the D-glucose residues are in b-(1! 4)linkages. The rigid chair structures can rotate relative to one another. (b) Schematic drawing shows the inter- andintra-molecular hydrogen bonds between two parallel cellulose chains (from Nelson et al. [90, p. 249, Fig. 7–16]).


has been removed. Depending on the species, wood contains on a dry basis about 40–55%cellulose, 15–35% lignin, and 25–40% hemicelluloses [92]. The plant cell wall is a compositeof cellulose, lignin, and hemicelluloses which provides strength, rigidity, and prevents theswelling of the cell. The plant cell wall is discussed in Section 9.2.

6. Biological ceramics and ceramic composites

We follow the Wegst–Ashby classification in Sections 6–9, and present four classes ofbiological materials given in Fig. 1. For each class, we provide illustrative examples.

6.1. Sponge spicules

Sea sponges have often long rods (spicules) that protrude out. Their outstanding flex-ural toughness was first discovered by Levi et al. [93] who were able to bend a 1 m rod,having a diameter similar to a pencil, into a full circle. This deformation was fully revers-ible. Additionally, these rods are multifunctional and carry light. The optical propertieswere studied by Aizenberg et al. [94]. The structural hierarchy of the hexactinellid spongespicule is a remarkable example of nature’s ability to create sophisticated composites fromrelatively weak constituent materials. These spicules, which are found at the base of thesilica basket (seen in Fig. 34), highly resemble the fragile fibers which are used in modernfiber optics [95]. They will be discussed in Section 11. As seen in Fig. 35a, the microcom-posite design of this natural rod creates remarkable toughness especially in comparison toits industrial counterpart [94]. Fig. 35b shows a fractured Hexactinellid spicule (much

Fig. 33. The unit cell of crystalline cellulose (from Bledzki and Gassan [91, p. 231]).


smaller than the one studied by Levi et al. [93]) that reveals its structure. This spicule,which has been studied by Mayer and Sarikaya [38], is a cylindrical amorphous silicarod and has an ‘onion skin’ type structure which e!ectively arrests cracks and providesan increased flexural strength. Fig. 35a shows the flexural stress as a function of strain.The spicule response is compared with that of a synthetic monolithic silica rod. The break-ing stress of the spicule is four times higher than the monolithic silica. Additionally, animportant di!erence exists between the two: whereas the monolithic silica breaks in a sin-gle catastrophic event, the spicule breaks ‘gracefully’ with progressive load drops. This isthe direct result of the arrest of the fracture at the ‘onion’ layers. These intersilica layerscontain an organic component which has been identified by Cha and coworkers [83] as sil-icatein (meaning a silica-based protein).

Each silica rod is composed of a central pure silica core of approximately 2 lm in diam-eter surrounded by concentric striated shells of decreasing thickness [95]. The individualshells are separated by the thin organic layer (silicatein) which is marked by an arrowin Fig. 36b. The mechanical toughness of the material is highly dependent on the striatedlayers as they o!er crack deflection and energy absorption at their interfaces [93,94,96].The gradual reduction in the thickness of the layers as the radius is increased is clearly evi-dent in Fig. 36c.

Another fascinating spicule from a sea sponge is the Hyalonema sieboldi. This is alsocalled glass rope sponge and it contains anchoring spicules that are remarkable for theirsize (up to 1 m), durability, flexibility, and optical properties. Fig. 37a shows a basalspicule in H. sieboldi. It can be seen how it can be into a circle. Ehrlich and Worch [68]

Fig. 34. Glass sponge, showing the basket cage and the spicules (from Sundar et al. [95]).


describe their structure with emphasis on the elaborate collagenous network, which has atwisted plywood structure quite di!erent from the one exhibited by the Hexactinellidasponge. This can be seen in Fig. 37b, this collagen acts as mediation for the nucleationand growth of the amorphous silica. Ehrlich and Worch [68] comment on the evolutionaryaspects. Silicon is thought to have been a first stage in the inorganic to organic evolution-ary process, leading finally to carbon based organisms. Silicon is the most common of theelements on the surface of the earth after oxygen and the ocean floors are covered withamorphous silica sediment, most of which results form living organisms. Ehrlich andcoworkers [97,98] indicate that chitin is a component of the skeletal fibers of marinesponges, which have intricate elaborate structures.

Fig. 35. (a) Flexural stress vs. strain for monolithic (synthetic) and for sea spicule; (b) Fractured spicule on seasponge (courtesy of G. Mayer, U. Washington [38]).


6.2. Shells

Shells have fascinated mankind since prehistory. They have been found in Neanderthalburial sites, evidencing the attraction they have exerted. Indeed, Aristotle and Pliny theElder were among the first to write about shells; it seems that it was Aristotle who coinedthe name ‘‘Mollusca,’’ meaning soft-bodied. Two aspects of seashells are of estheticsignificance:

• The mother-of-pearl coloration, which results from the interference of visible light withthe tiles that comprise nacre (!0.5 lm thickness, approximately equal to thewavelength).

• Their multiple and intricate shapes.

D’Arcy Thompson showed that this shape is, for many shells, a derivative of the log-arithmic spiral [1]. Fig. 38a shows the top of an abalone shell. There are two spiral linesindicated; one follows the pattern of perforations which circulate the water and areclosed as the shell grows. The second represents the markings of successive growth sur-faces. The logarithmic spiral which exists in many shells is shown in Fig. 38b. It can beunderstood as formed by the aggregation of mineral, composed of two vectors: one withthe radial direction (d r

*), and one in the tangential direction (d s

*). If the ratio of the

magnitude of these two vectors is constant throughout the growth process, the angle ais unchanged:

Fig. 36. Microstructure of a sponge spicule (from Aizenberg et al. [94]).


tan a $ drds

"15#

But, we have

ds ) rdh "16#

where r is the radial coordinate of a point along the curve and h its angular coordinate.Substituting Eq. (15) into (16)

drr$ dh tan a "17#

Fig. 37. (a) Unique flexibility of basal spicules of H. sieboldi. (b) SEM micrograph showing the twisted plywoodorientation of collagen microfibrils (from Ehrlich and Worch [68]).


Integrating

ln r $ h tan a% C "18#

Or

r $ eCeh tan a "19#

Fig. 38. (a) A photograph of abalone shell. There are two lines indicating the logarithmic spiral fashion ofgrowth. (b) The growth vector of a logarithmic spiral consists of two vectors, one in tangential direction, the otherin the radial direction. The ratio of the magnitude of these two vectors is constant throughout the growth process,and the angle a remains unchanged.


Eq. (19) expresses the logarithmic spiral curve. Skalak et al. [100] present a detailedanalysis.

Other than their esthetic attributes, these shells provide the primary means of protec-tion for the soft bodies of the animals they house. They are permanent encasements ofbody armor, which must be strong enough to withstand the impact and compression capa-bilities of a sea of predators. Mollusk shells consist of one or more ceramic phases andsmall fraction (0.1–5%) proteins. These ceramic phases alone, i.e. calcium carbonate(CaCO3), are not suitable as structural materials because of their inherent brittleness.However, when combined into these intricate natural structures a resulting biocompositewith outstanding mechanical properties is created. This is true for many biological mate-rials [38]. The micro-structure and macro-structure of these shells plays a significant role inincreasing the toughness of an otherwise brittle ceramic base. Five main types of molluskshell structures have been identified. They are nacreous (flat tablets), crossed lamellar (ply-wood-like), prismatic (polygonal columns), foliated (long thin crystals in overlapping lay-ers) and homogeneous (fine-scale rubble), which can, in some cases, occur alongside eachother. In the following sections, we discuss the growth and formation of some of thesestructures, and the mechanisms through which they achieve their amazing mechanicalproperties.

6.2.1. Nacreous shellsThe schematic of the longitudinal cross-section (Fig. 39) of the abalone shell (Haliotis)

shows two types of microstructure: an outer prismatic layer (calcite) and an inner nacreouslayer (aragonite) as observed by Nakahara et al. [101]. The two forms of CaCO3 have thestructures; calcite (rhombohedral) and aragonite (orthorhombic). The structure of nacre(the inside portion of the shell, shown in Fig. 39) within the shells of abalone consistsof a tiled structure of crystalline aragonite; moreover there is a very high degree of crys-tallographic texture characterized by a nearly perfect ‘‘c-axis’’ alignment normal to theplane of the tiles. Fig. 40a shows schematically the brick and mortar microstructure foundin abalone nacre [102], and Fig. 40b shows the layered structure in a TEM micrograph[103]. In Fig. 40c the ‘‘c-axis’’ orientation is shown. The staggering of tiles in adjacent lay-ers is also clearly visible.

Periodic growth arrests create mesolayers that also play a critical role in the mechanicalproperties and are powerful crack deflectors. Fig. 41 shows this structures. Layers of visco-plastic material separate the thicker layers (mesolayers) which are approximately 300 lmthick and an inorganic layer with a thickness of about 20 lm. These layers were identifiedby Menig et al. [8] but are not often mentioned in other reports dealing with the

Fig. 39. Structure of typical abalone shell (adapted from Zaremba et al. [108]).


mechanical properties of abalone. It is thought that these thick organic layers form inabalone grown in the sea during periods in which there is little calcification.

In the case of the abalone nacre, the mineral phase corresponds to approximately95 wt% of the total composite. The deposition of a protein layer of approximately

Fig. 40. (a) Brick and mortar microstructure of nacre (schematically) (from Sarikaya [102]). (b) TEMmicrographof layered structure of abalone (courtesy of K.S. Vecchio, University of California, San Diego [103]). (c)Microstructure of abalone nacre showing tiles layers staggered one on top of the other with the same c-axisorientation.

Fig. 41. Mesostructure of abalone shell, showing growth bands (from Menig et al. [8]).


20–30 nm is intercalated aragonite platelets, which are remarkably consistent in dimensionfor each animal regardless of age [9]. However, there are di!erences when examining vary-ing species of nacre forming animals: the thickness of the tiles in the abalone shells isapproximately 0.5 lm, as seen in Fig. 42a, while it is around 0.3 lm for a bivalve shellfound in the Araguaia River (Brazil), thousands of miles from the ocean (Fig. 42b).

Fig. 42. Nacreous tile structures; (a) Abalone (H. rufescens) from Southern California; (b) Bivalve shell fromAraguaia River, Brazil.

Fig. 43. ‘‘Christmas tree’’ pattern observed on the growth surface of steady state tiled aragonite nacre.


6.2.1.1. Growth of abalone (Haliotis rufescens) nacre. The growth of the red abalone shellhas been the subject of considerable study starting in as early as the 1950s with Wada[104,105], continuing with Watabe and Wilbur [106], Bevelander and Nakahara [107]and followed by many others. The work by the UC Santa Barbara group [64,82,108–114] represents one of the most comprehensive e!orts. Shell growth begins with the

Fig. 44. (a) Macrostructural view of a cross-section of the H. rufescens shell. Growth bands are observedseparating larger regions of nacre, (b) SEM micrograph of fracture surface; direction of growth marked witharrow.


secretion of proteins that mediate the initial precipitation of calcite, followed by a phasetransition from calcite to aragonite. There are at least seven proteins involved in the pro-cess. As steady state tiled aragonite growth is reached, nacre deposition occurs through thesuccessive arrest of mineral deposition by means of a protein-mediated mechanism; this isfollowed by the subsequent re-initiation of mineral growth on the new surface layer. Thistakes place in the ‘‘Christmas-tree pattern’’ as seen in Fig. 43.

Additional macro-scale structure was identified as the periodic interruption of aragonitictile growth in the form of mesolayers, possibly being attributed to sporadic interruptions inthe animal’s diet [8,9]. In nacre there is a synergy of structural hierarchy pertaining to manydi!erent length scales. The following discussion begins with the formation of macro-scaledelements, followed by micro-structural formation, and finally the growth of nanoscale com-ponent of the shell. Fig. 44a provides a macrostructural view of a cross-section of the innernacreous layer. Organic bands approximately 8 lm thick can be seen separating larger,300 lm thick, regions of nacre. These ‘‘mesolayers’’ mark interruptions in nacre growth,

Fig. 45. Summary of sequential growth from flat pearl and trepanning experiments (from Lin et al. [115]).


and thus are therefore also called growth bands. The inorganic CaCO3 undergoes morpho-logical changes before and after the interrupting growth bands [115]. As seen in Fig. 44b,five regions can be identified (direction of growth marked by arrow): tiled (A); block-likearagonite (B); organic/inorganic mix (C); organic (D); and spherulitic (E). The growthsequence is described in greater detail by Lin andMeyers [9]. In Fig. 44b, the growth occursfrom bottom to top. Prior to arrest of growth, the characteristic tiles are replaced by ablock-like structure (B). This is followed by the massive deposition of the organic layer,which is initially intermediated with mineralized regions. At the end of the mesolayer, whenmineralization starts again, a layer comprised of a spherulitic structure is observed. Boththe ‘‘flat pearl’’ technique, first introduced by Wada et al. [116,117] then further developedby the UC Santa Barbara group [113], and the ‘‘trepanning’’ technique in which foreign sec-tions of nacre are introduced into the growth surface were used by Lin et al. [115] to observethe various formations following steady state growth interruption. The results of thesequential growth study are presented in Fig. 45.

Two weeks after implantation, the precursor aragonite has spread across the entire sub-strate. None of the original implantation is left exposed. As seen in the lower half ofFig. 45, the morphology of deposited mineral transitions to spherulitic aragonite betweenthe second and third week. It was earlier thought that the spherulitic layer was calcitic[108], but Su et al. [112] incontrovertibly identified it as aragonitic; this was also laterreconfirmed by Lin et al. [115].

After three weeks of implantation the tops of each spherulitic bundle appear flattened.This is thought to be the result of a constant pressure or a rubbing force exerted by themantle of the animal itself. Indeed, it is proposed that the animal forms the structure ofthe shell through a mechanical-chemical action. The self-assembly of aragonite in nacredoes not translate into the overall architecture of the shell; the animal continuously moldsit. The animal has the ability to apply a significant amount of binding force to keep itselfattached to virtually any surface. This force translates to an approximately equal andopposite force applied normal to the growth surface of the shell. The epithelial layer ofthe mantle sits directly over the growth surface. As the animal moves along a rock or awall it twists itself in a rotating manner. The epithelial skin slides back and forth alongthe shell producing a sanding e!ect over the growing mineral structures. This mechanicalflattening of the growing surface occurs throughout the nacre deposition region.

After four weeks of implantation, the spherulites are fully formed as a result of thedivergent growth of aragonite columns along the fast growing c-axis direction. Thecross-sectional view of a growth band, shown in Fig. 44, shows the divergent growth ofthese columns. They spread apart into a lower density as growth continues after five weeksof implantation. Between five and six weeks of implantation the aragonite morphologytransitions towards the regular tiled aragonite microstructure as shown at the top ofFig. 45. It is hypothesized that this transition may occur as the ends of each spheruliticneedle become nucleation sites for aragonite tiles. The intermittent deposition of theorganic matrix which is believed to inhibit crystal growth [118] molds the spherulitic ara-gonite needles into an increasingly laminate structure, eventually reaching the steady-statearagonite tile formation. The ‘‘Christmas tree’’ like growth fields are associated with tiledaragonite growth [82,108,113,114] and can be seen in Fig. 46.

Fig. 46a shows a low magnification view, and it is seen that the ceramic phase nucleatesrandomly over the proteinaceous layer. Closer observation, shown in Fig. 46b reveals the‘‘Christmas tree’’ pattern described earlier by Shen et al. [82] and Fritz and Morse [114].


However, it should be noticed that the center-to-center distance is less than the tile size innatural abalone, which is 10 lm. It is possible that the glass from the implants providesgreater areal density of nucleation sites; however, similar spacing was observed with thetrepanning method [115]. A schematic drawing of adjacent ‘‘Christmas trees’’ is shownin Fig. 46 (c). Each tile is smaller than the one below it.

Fig. 47 shows a hypothetical description of the sequence of tile growth, as it has beenthought to occur during steady state deposition. First, a proteinaceous layer (possibly, thebeta conformation of Addadi et al. [62]) is deposited. The aragonite crystals nucleate andgrow on it, with a characteristic spacing. They have the orthorhombic structure with the‘‘c’’ direction is perpendicular to the protein plane [3]. In the absence of proteins, this is therapid growth direction. Addadi and Weiner [61] and Addadi et al. [62] demonstrated thatthere is stereoselective adsorption of proteins in the growth of calcite crystals; this resultsin a slowing down of growth in the ‘‘c’’ direction and completely alters the final shape ofthe crystals. Addadi et al. [62] also showed that the (001) plane of calcite is the one thatforms on the protein layer. The similarity between the two polymorphs (calcite and arago-nite) of calcium carbonate is a strong indication that a similar mechanism might be oper-ating. It is speculated that the host animals produce the proteins that arrest growth in the

Fig. 46. Growth on 15 mm slide after 24 days; (a) low-magnification SEM; (b) high-magnification SEM; (c)schematic drawing showing the same crystallographic orientation.


‘‘c’’ direction in a periodic manner. Thus, the (001) growth is periodically arrested. It wasearlier thought that new aragonite tiles nucleate at the growth surfaces, on the beta con-formation layer. This occurs in parallel with lateral growth. More recent advances showthat aragonite does not nucleate on the beta layer, rather mineral growth continuesthrough pores in the organic membrane, allowing sites on which new tiles can form. In thisfashion, successive ‘‘terraces’’ are formed and propagate. The resulting configuration is the‘‘Christmas tree’’ morphology reported by Simkiss and Wilbur [119] and in greater detailby Belcher [109] and Fritz et al. [113].

The organic layers covering each tile layer may play an important role by providing thesca!olding for formation. First observed and described by Nakahara et al. [120,121], theyexist and are in place before the growth of aragonite tile is complete. Fig. 48a representsthe possible environment surrounding aragonite tiles with the presence of the organic scaf-folding. The calcium and carbonate ions can penetrate through the organic layer depositedby the epithelium. Electron microscopy of the resulting growth surfaces shows columns ofsequential aragonite tiles (Fig. 48b).

The mechanism of arresting and initiating growth of subsequent layers of aragonite hasled to some debate pertaining to the interface between tile layers. The apparent crystallo-graphic alignment along the c-axis indicated a mineral connection between tiles. Initially,Sarikaya [122] reported a central core along the ‘‘Christmas tree’’ trunk. This central corewould be responsible for triggering lateral growth. Song et al. [123,124], on the other hand,report a large number of bridges in each tile. The bridges traverse the organic layers, which

Fig. 47. Hypothetical growth mechanism with periodic injection of proteins arresting growth in ‘‘c’’ direction.(a,b) Protein deposition causing the arrest of crystallographic growth in the ‘‘c’’ direction; (c) second growth spurtafter deposition of beta sheet and nucleation; (d) first aragonite plates are butted together while growth of secondlayer continues in ‘‘a, b’’ direction; (e) nucleation of third layer as second layer growth continues in ‘‘a’’ direction(from Lin and Meyers [9]).


Fig. 48. Growth of nacreous tiles by terraced cone mechanism; (a) Schematic of growth mechanism showingintercalation of mineral and organic layers; (b) SEM of arrested growth showing partially grown tiles (arrow A)and organic layer (arrow B).

Fig. 49. Schematic representation of mineral bridges connecting sequential aragonite tiles layers.


are porous. They observed a higher concentration of bridges in the central region of thetiles; this is shown schematically in Fig. 49. Having been first described by Scha!eret al. [125], they are responsible for transmitting the crystallographic orientation fromlayer to layer. Atomic force microscopy [125], transmission electron microscopy[124,115], and scanning electron microscopy [115] have been used to observe the existenceof mineral bridges in abalone nacre; the results are presented in Fig. 50(a–d). Fig. 50ashows a TEM of a tile with the lighter regions marked by arrows being identified by Songet al. [124] as bridges. Fig. 50b shows the tiles (boundaries dark). The small white spots aresupposedly remnants of bridges. Fig. 50c and d show cross-sectional regions (SEM andTEM, respectively). The bridges are marked by arrows.

Fig. 51a represents the sequence in which growth occurs through mineral bridges. Thegrowth sequence is as follows; (i) organic sca!olding forms as interlamellar membranesbetween the layers of tiles arresting c-direction growth, (ii) a new tile begins growth

Fig. 50. (a) TEM view of mineral bridges on tile surfaces (from Song et al. [123,124]), (b) AFM image of mineralbridge reminents on tile surface (from Scha!er et al. [125]), (c) SEM micrograph showing mineral bridges betweentiles after deproteination (from Lin et al. [115]), (d) TEM micrograph of nacre cross-section showing mineralbridges (from Lin et al. [115]).


through the porous membrane, (iii) the new tile grows in every direction, but faster alongthe c-axis, (iv) a new porous organic membrane is deposited, arresting c-axis growth of thenew tile while allowing continued a and b-axis; growth, mineral bridges begin to protrudethrough the second organic membrane while sub-membrane tiles continue to grow alongthe a and b-axis, sub-membrane tiles abut against each other; a third tile begins to growabove the membrane. As shown, the bridges are believed to be the continuation of min-eral growth in the c-axis from a previous layer of tiles. They protrude through thegrowth arresting layers of proteins, creating a site on the covering organic layer wheremineralization can continue. These mineral bridges are the seed upon which the next tileforms.

A detailed view of mineral bridges enabling growth through a permeable organic mem-brane is shown in Fig. 51b. Holes in the organic nanolayer, which have been identified byScha!er et al. [125], are thought to be the channels through which growth continues. Min-eral growth above the membrane is faster than growth in the membrane holes because ofthe increase in contact area with surrounding calcium and carbonate ions. Since theseholes are small (30–50 nm diameter) the flow of ions is more di"cult, resulting in a reduc-tion of growth velocity to V1 * V2 (Fig. 51b). V2 is the unimpeded growth velocity in the c

Fig. 51. (a) Growth sequence through mineral bridges (b) Detailed view of mineral bridges forming through holesin organic membranes.


direction. The supply of Ca2+ and CO2&3 ions to the growth front is enabled by their flow

through the holes in the membranes. This explains why the tiles have a width to thicknessratio of approximately 20 whereas the growth velocity in the orthorhombic c direction ismuch higher than in the a and b direction.

While in gastropods the nucleation of aragonite tiles occurs in the Christmas tree pat-tern described above, bivalve mineralization takes place with tablets o!set with respect tolayers above and below them. Fig. 52 from Wang et al. [126] compares the two nacre struc-tures as tile separation occurs: (a) in gastropod (abalone) shell where columns of whitemarkings (identified with white arrows) indicate separation, and (b) in bivalves (pearl oys-ter) shell where tile location is o!set from preceding layers and separation is more random.

Cartwright et al. [127] compare di!erences in microstructures between gastropods andbivalves and attribute them to variations in growth dynamics. In gastropods there are alarge number of holes that enable the growth, therefore a ‘‘Christmas tree’’ or terracedcone stacking of tiles is possible. In bivalves a smaller number of holes exist, most of whichare filled with proteins and not mineral. There appears to be no direct evidence of mineralbridges. However heteroepitaxy is required for the tiles to retain the same orientation.Cartwright et al. [127] suggest that there are more widely spaced bridges in bivalves, asshown in Fig. 53. There are two bridges per tile, causing the heteroepitaxial growth to dic-tate a random stacking of subsequent tiles.

6.2.1.2. Mechanical properties of abalone nacre. As a result of the highly ordered hierarchi-cal structure [3,4,70,99,128–131], biocomposites generally exhibit excellent mechanicalproperties. We shall describe the mechanical characteristics of the shell, then examine eachscale of structural design and how they contribute to the strength and toughness of nacredescribed above, beginning with the mesolayers, followed by the aragonite tiles, and finallyending with the interface between tile layers.

Currey [132] was the first to perform measurements of mechanical properties of nacrefrom a variety of bivalves, gastropods and cephalopods. He obtained a fracture strength inbending varying between 56 and 116 MPa. This was followed by Jackson et al. [133] whoused nacre from the shell of a bivalve mollusk, Pinctada. They report a Young’s modulusof approximately 70 GPa for dry and 60 GPa for wet samples; the tensile strength of nacrewas found to be 170 MPa for dry and 140 MPa for wet samples. The work of fracture var-ied from 350 to 1240 J/m2, depending on the span-to-depth ratio and the degree of hydra-tion, wet nacre showing superior toughness by associated introduction of plastic work. Incontrast, monolithic CaCO3 showed a work of fracture that was about 3000 times less

Fig. 52. Tile separation occurs; (a) in a gastropod (abalone) shells where tiles are formed in columns, and (b) in abivalves (pearl oyster) shells where tile location is o!set from preceding layers (from Wang et al. [126]).


than that of the composite nacre material. It should be noted that this work of fracture isnot identical to the toughness measured by Sarikaya et al. [134]. The work-of-fracture isthe area under the stress–strain curve and is deeply a!ected by gradual, graceful fracture,whereas the fracture toughness does not incorporate this entire process. Thus, one shouldbe careful when considering this number. Early studies show indications of the low span-to-depth ratios of tiles contributing to fracture toughness [129]. Jackson et al. [133] con-cluded that water a!ects the Young’s modulus and tensile strength by reducing the shearmodulus and shear strength of the organic matrix which comprises less than 5 wt% of thetotal composite. The toughness is enhanced by water, which plasticizes the organic matrix,resulting in greater crack blunting and deflection abilities. In contrast with more tradi-tional brittle ceramics, such as Al2O3, or high toughness ceramics, such as ZrO2, the crackpropagation behavior in nacre reveals that there is a high degree of tortuosity.

Sarikaya et al. [134] conducted mechanical tests on H. rufescens (red abalone) withsquare cross-sections. They performed fracture strength rf (tension) and fracture tough-ness KIC tests on single straight notched samples in 4-point and 3-point bending modes,respectively, in transverse direction, i.e. perpendicular to the shell plane. A fracturestrength of 185 ± 20 MPa and a fracture toughness of 8 ± 3 MPa m1/2 was found. Thisis an eightfold increase in toughness over monolithic CaCO3. The scatter is explained withthe natural defects in the nacre and the somewhat curved shape of the layers. The KIC andrf value of synthetically produced monolithic CaCO3 is 20–30 times less than the averagevalue of nacre. The specific flexural strength of CaCO3 is 10 MPa/g cm&3.

Menig et al. [8] measured the compressive strength of red abalone and found consider-able variation. Weibull statistics [135] were successfully applied. This is within the rangefor synthetic ceramics. Presented in Fig. 54 are the results for tests on abalone nacre (a)in quasi-static compression, with failure probabilities of 50% being reached at 235 MPaand 540 MPa with loading parallel and perpendicular to layered structure, respectively,and (b) dynamic compression with 50% failure probabilities for the abalone shell foundat 548 MPa and 735 MPa with the layered structure parallel and perpendicular to loading,respectively. Fig. 55 shows the Weibull analysis of nacre in tension with load perpendicularto layers. Here a 50% failure probability was determined at only 5 MPa. The Weibullmoduli in tension and compression are similar: 2 and 1.8–2.47, respectively. However,

Fig. 53. Growth sequence in bivalve nacre (from Cartwright and Checa [127]).


the di!erence in strength is dramatic and much higher than in conventional brittle mate-rials. The ratio between compressive and tensile strength is on the order of 100, whereas inbrittle materials it varies between 8 and 12. This di!erence is indeed striking, especially ifone considers the tensile strength parallel to the layer plane, on the order of 140–170 MPa[133], which is approximately two-thirds the compressive strength. Other work by Barth-elat et al. [152] found the tensile strength of nacre to be closer to 100 MPa, which is stilljust below half the compressive strength. It can be concluded that the shell sacrifices tensilestrength in the perpendicular direction to the tiles to use it in the parallel direction. Fig. 56summarizes the strength of nacre with respect to various loading directions. The unique

Fig. 54. Weibull plots of abalone nacre in; (a) quasi-static, and (b) dynamic compressive loading (from Meniget al. [8]).


strength anisotropy perpendicular to the layers (5 MPa vs. 540 MPa) is remarkable andwill be discussed later. Another marked characteristic is the greater compressive strengthwhen loading is applied perpendicular rather then parallel to the tiles. This is due to thephenomena of axial splitting and microbuckling (kinking) when loading is applied parallelto the tiles. The relatively small di!erence in tensile and compressive strength (170 MPa vs.230 MPa) in this direction of loading is directly related to the high toughness. Both theseaspects are discussed below.

The abalone exhibits orientation dependence of strength as well as significant strain-ratesensitivity; the failure strength at loading rates of 104 GPa/s was approximately 50% higherthan the quasi-static strength. Compressive strength when loaded perpendicular to the shell

Fig. 55. Weibull distribution of tensile with force direction perpendicular to layered structure (from Meyers et al.[141]).

Fig. 56. Strength of nacre with respect to loading direction.


surface was approximately 50% higher than parallel to the shell surface. Quasi-static com-pressive failure in both shells occurred gradually, in ‘‘graceful failure’’. The shear strengthof the organic/ceramic interfaces of H. rufescens was determined by means of a shear testand was found to be approximately 30 MPa. Considerable inelastic deformation of theselayers (up to a shear strain of 0.4) preceded failure.

Upon compression parallel to the plane of the tiles, an interesting phenomenonobserved previously in synthetic composites was seen along the mesolayers (previouslydescribed): plastic microbuckling. This mode of damage involves the formation of a regionof sliding and of a knee. Fig. 57 shows a plastic microbuckling event. Plastic microbuck-ling, which is a mechanism to decrease the overall strain energy, was observed in a signif-icant fraction of the specimens. Plastic microbuckling is a common occurrence in thecompressive failure of fiber-reinforced composites when loading is parallel to the rein-forcement. The coordinated sliding of layer segments of the same approximate lengthby a shear strain c produces an overall rotation of the specimen in the region with adecrease in length. Fig. 57 shows a characteristic microbuckling region. The angle a wasmeasured and found to be approximately 35". The ideal angle, which facilitates micro-buckling according to Argon, is 45" [136].

The angle h (Fig. 57) varies between approximately 25" and 15" and is determined bythe interlamellar sliding. This angle is consistent with the shear strain of 0.45 betweenlamellae observed in Fig. 58. The shear strain associated with the rotation h in Fig. 57is tan h = c = 0.47. Hence, the rotation h in kinking is limited by the maximum shearstrain, equal to 0.45. If this kinking rotation were to exceed 0.45, fracture along the slidinginterfaces would occur. It is estimated the shear strain undergone by the organic layersprior to failure. The shear strain c0 is

c0 $cf

"20#

where f is the fraction of organic layer, which has an approximate value of 0.05, providingc0 ) 9. The results by Menig et al. [8] are of the same order of magnitude as the ones re-ported by Sarikaya [134]. These results were applied to existing kinking theories [136,137].

Fig. 57. Mechanisms of damage accumulation in nacreous region of abalone through plastic microbuckling.


The Argon [136] formalism for kinking based on an energetic analysis, was applied. Theplastic work done inside the band (W) is equated to the elastic energy stored at the extrem-ities (DE1) of the band and the energy outside the band (DE2) that opposes its expansion:

DE1 % DE2 & W $ 0 "21#

This leads to

r ) sh0

1% bGcDh2pas"1& m#

ln2pas"1& m#

bGcDh

$ %% ErDh

48strb

( )2" #

"22#

where s is the shear strength of the matrix, h0 is the angle between the reinforcement andthe loading axis, Er is Young’s modulus of the reinforcement, tr is the lamella thickness, Gc

is the shear modulus of the composite, t is Poisson’s ratio, and a and b are the kink nucleusdimensions. Fleck et al. [138] and Jelf and Fleck [139] further developed this treatment.

Budiansky [137], using a perturbation analysis, developed the following expression forthe ratio between the thicknesses of kink bands and the spacing between reinforcementunits (w/d):

wd$ p

4

2syCE

$ %&1=3

"23#

where E is the Young’s modulus of the fibers and C is their volume fraction. It is interest-ing to note that Eq. (23) predicts a decrease in w/d with increasing sy.

These formalisms for microbuckling were applied to the results of Menig et al. [8] andenable some conclusions to be drawn regarding the kink stress and spacing of the slipunits. Fig. 59a shows the predicted compressive kinking stress for abalone as a functionof misalignment angle. It can be seen that the strength is highly sensitive to the angle a.Fig. 59b using the Budiansky equation adapted to the abalone geometry shows the kinkband thickness (w) as a function of strain rate. The results by Menig et al. [8], carriedout at di!erent strain rates, confirmed the Budiansky prediction. Two parameters wereused: the mesolayer and microlayer thicknesses. The experimental results shown in

Fig. 58. Experimental shear stress-shear strain curve for nacre (from Menig et al. [8]).


Fig. 59b fall in the middle, showing that both the mesolayers and platelets (microlayers)take part in kinking.

Another significant mechanism of toughening is crack deflection at both the meso- andmicro-scale. The e!ect of the viscoelastic organic interruptions between mesolayers or evenindividual aragonite tiles is to provide a crack deflection layer so that it becomes more dif-ficult for the cracks to propagate through the composite. Therefore the composite is supe-rior to the monolithic material, in which a propagating crack has no barriers. Jackson

Fig. 59. Application to shell microbuckling (from Menig et al. [8]) of (a) Argon [136] analysis for kink stressformation and (b) Budiansky [137] formalism for the kink-band thickness prediction.

Fig. 60. (a) Cross-section of abalone shell showing how a crack, starting at the left is deflected by viscoplasticlayer between calcium carbonate lamellae. (b) Schematic drawing showing arrangement of calcium carbonate innacre, forming a miniature ‘‘brick and mortar’’ structure (from Meyers and Chawla [161]).


et al. [133] correctly recognized that the increase in path length, created through deflectionof cracks, is responsible for enhanced work of fracture. The two levels of the structure pre-sented in Fig. 60 can be seen engaging in this mechanism: (a) mesolayers provide crackdeflection, (b) at a smaller scale the tile layers force cracks in a tortuous path. This andseveral other toughening mechanisms have been proposed [134] including: (a) crack blunt-ing/branching, (b) microcrack formation, (c) plate pull out, (d) crack bridging (ligamentformation), and (e) sliding of CaCO3 layers. The high degree of crack tortuosity in theseshells may be due mainly to crack blunting and branching. However, it is reported that themany orders of magnitude increase in toughness cannot only be caused by tortuosity.Therefore, it is possible that the major toughening mechanisms are sliding and ligamentformation [140]. Fig. 61 shows tensile failure along the direction of the tiles. The tensilestrength of the tiles is such that they do not in general break, but slide along their inter-faces. The tile sliding is represented in Fig. 61b. This is accomplished by the viscoplasticdeformation of the organic layer and/or by the shearing of the mineral ligaments travers-ing the organic phase.

The organic phase, is not a monolithic material but possesses a structure. The centerregion is structurally more rigid with high chitin content, as mentioned in Section 5.

Fig. 61. Mechanisms of damage accumulation in nacreous region of abalone through tile pullout.

Fig. 62. Various models for the proteinaceous layer.


Aspartic acid is a major constituent of the acid soluble components. Other constituents areglutamic acid, serine, glycine, alamine. Shen et al. [82] reported the characterization of thecDNA coding for ‘‘Lustrin A’’ which is a protein they have identified within the nacreouslayer of red abalone. Fig. 62 is a representation of the di!erent structures proposed for theorganic layer. Early models indicate the presence of a thin protein sheet (10–40 nm thick)sandwiched between the aragonite tiles. More complex models attempt to represent thecomposition of the organic matrix with a central b-chitin sheet sandwiched between b-pleated proteins which are in turn covered in acidic proteins which act as the interface

Fig. 63. Atomic force microscopy of organic layer; (a) overall view at low magnification showing outline ofhexagonal tiles; (b) high magnification showing linear chains and holes with !30 nm diameter (from Meyers et al.[141]).


between the organic and inorganic. Atomic force microscopy of nacre following EDTAdemineralization exposes the structure of the organic matrix, Fig. 63. Meyers et al. [141]obtained a biaxial elastic modulus of 100 Pa, by measuring the sagging of the membranebetween a tile spacing of 10 lm. This is indeed a very low value. This low value can only beexplained if the random network of protein chains in Fig. 63b can slide when tension isapplied to the membrane. The value of 100 Pa is an upper bound, and the range of elasticmoduli is comparable to that for living cells [142]. This value is also consistent with thehigh maximum tensile strains that the organic layer can undergo in tension. Belcher andGooch (Fig. 15.9) [143] quote a value of emax = 3 (equivalent to a maximum stretchk = e + 1 = 4). The calculations confirm that the organic layer material has a very smallsti!ness and is highly stretchable.

The interface between the organic phase and the aragonite may be critical in the shearstrength of the laminate components. Fig. 64 shows the unit cell. The (001) plane is thetop surface. The calcium atoms are black; the carbon atoms are black and smaller; theoxygen atoms are gray. As described by Weiner and coworkers [144–146] Fig. 64 showsthe aspartic acid-rich protein (Asp-Y)n, where Y is an amino acid bonding to the Ca2+ ionsof the aragonite structure. These proteins, in their turn, bond to the more rigid beta sheets.Addadi and Weiner [61] describe the phenomenon of stereoselectivity in considerabledetail and provide three possible explanations for it. They suggest that the asparticacid-rich protein binds to calcium atoms preferentially. Indeed the (001) plane of arago-nite is characterized by protruding calcium atoms.

Additional toughening mechanisms such as sliding of CaCO3 layers and organic liga-ment formation were thought to operate and were analyzed by Lin and Meyers [9].Fig. 65 shows the tensile strength of the aragonite phase as a function of crack size.The fracture toughness was taken as 1 MPa m1/2. It can be seen that, if one considersthe strength limited by flaw size, that it increases from values of 50 MPa for large flawsto 250 MPa for a flaw the size of a tile (10 lm). The strength of tiles increases with decreas-

Fig. 64. Unit cell of aragonite showing schematic position of (Asp-Y)n and b sheet. Notice protruding calciumions on (001) face; black atoms: Ca; small black: carbon; gray atoms: oxygen (courtesy of K.S. Vecchio, UCSD[103]).


ing size, and one can safely assume that it is higher than 250 MPa, for the given size. Thus,the values of tensile strength obtained by Menig et al. [8] (180 MPa from flexure tests) andWang et al. [126] (110 MPa) may be explained by viscoplastic flow of organic matrix orplastic failure of mineral bridges at the tile interface, starting at 10 MPa and proceedingthrough gradual increase, until separation occurs.

Evans et al. [147] and Wang et al. [126] proposed an alternative toughening mechanism:that nano-asperities on the aragonite tiles are responsible for the mechanical strength.These nano-asperities create frictional resistance to sliding, in a manner analogous torough fibers in composite material. They developed a mechanism that predicts the tensilemechanical strength based on these irregularities. These nano-asperities were modeled byBarthelat et al. [152], who carried out nanoindentation and FEM analysis of the aragonitecrystals. Bruet et al. [148] obtained, through nanoindentation and atomic force micros-copy, local measurements of the mechanical properties of the aragonite tiles: E = 79and 92 GPa and compressive strengths of 11 and 9 GPa for dry and seawater soaked tiles,respectively. This strength is much higher than that observed by Menig et al. [8] incompression tests (540 MPa). The Young modulus is consistent with values reported in lit-erature [9,133]. The source of inter-tile shear resistance is still a subject of significantdebate.

Meyers et al. [141] made observations indicating that the organic layer, while playing apivotal role in the growth of the aragonite crystals in the c direction (perpendicular to tilesurface), may have a minor role in the mechanical strength. The tensile strength in thedirection perpendicular to the layered structure can be explained by the presence of themineral bridges. These bridges, having a diameter of approximately 50 nm, have a tensilestrength no longer determined by the critical crack size, but by the theoretical strength.Their number is such that the tensile strength of the tiles (parallel to the tile/shell surfaceplane) is optimized for the tile thickness of 0.5 lm, as shown by Lin and Meyers [9]. Ahigher number of bridges would result in tensile fracture of the tiles with loss of the crack

Fig. 65. Critical stress as a function of flaw size for aragonite [KIc = 1 MPa m1/2] (from Lin and Meyers [9]).


deflection mechanism. This is a viable explanation for the small fraction of asperities thatare bridges.

Meyers et al. [141] estimate the tensile strength of the individual mineral bridges byapplying the fracture mechanics equation to aragonite. Consistent with recent analysesby Gao et al. [149], Ji and Gao [150], and Ji et al. [151], the mineral bridges have sizesin the nanometer range. The maximum stress, rfr, as a function of flaw size, 2a, can beestimated, to a first approximation, to be

rfr $KIc******pa

p "24#

where KIc is the fracture toughness. However, the strength is also limited by the theoreticaltensile strength, which can be approximated as [149]:

rth $E30

"25#

We assume that KIc = 1 MPa m1/2, E = 100 GPa, and that 2a = D, where D is the speci-men diameter. Eqs. (24) and (25) intersect for a = 28 nm (D = 56 nm). This is indeed sur-prising, and shows that specimens of this and lower diameter can reach the theoreticalstrength. This is in agreement with the experimental results: the holes in the organic layerand asperities/bridge diameters are around 50 nm. Recent analyses [123,124,149] also ar-rive at similar values.

It is possible to calculate the fraction of the tile surface consisting of mineral bridges, f.Knowing that the tensile strength is rt and assuming that the bridges fail at rth, we have

f $ rt

rth"26#

The number of bridges per tile, n, can be calculated from

f $ nAB

AT"27#

Fig. 66. Calculated number of mineral bridges per tile as a function of bridge diameter.


where AB is the cross-sectional area of each bridge and AT is the area of a tile. Thus

n $ rtAT

rthAB"28#

Assuming that the tiles have a diameter of 10 lm and that the bridges have a diameterof 50 nm (the approximate observed value), one obtains, for rt = 3 MPa (the value foundby Meyers et al. [141]) and rth = 3.3 GPa, n = 36. Fig. 66 shows the relationship betweenmineral bridge diameter and the number of mineral bridges through Eq. (28). The numberof bridges calculated above is surprisingly close to the measurements by Song et al.[123,124]: 35 6 n 6 45. However, the interpretation of the results reported by Songet al. [123,124] is not clear. This result strongly suggests that mineral bridges can, by them-selves, provide the bonding between adjacent tiles.

The number of asperities seen in Fig. 67 exceeds considerably the values for bridges cal-culated herein and measured by Song et al. [123,124]. The estimated density is 60/lm2

(5000/tile). One conclusion that can be drawn is that a large number of asperities areindeed incomplete bridges and that these bridges are a small but important fraction ofthe protuberances.

Fig. 67. (a) Asperities (a fraction of which are remnants of mineral bridges) and (b) mineral bridges (marked byarrows) between tile layers.


The three models for the inter-tile region are shown in Fig. 68. The asperity model byEvans et al. [147] and Wang et al. [126] is represented in Fig. 68a. Fig. 68b shows the vis-coelastic glue model according to which the tensile strength is the result of stretching ofmolecular chains whose ends are attached to surfaces of adjacent tiles. Fig. 68c showsthe mineral bridge model, consistent with our observations. The sliding of adjacent tilesrequires the breaking of bridges and the subsequent frictional resistance, in a mode akinto the Wang–Evans [126,147] mechanism. It is possible that all three mechanisms act ina synergetic fashion in which broken bridges act as asperities which are further reinforcedby the viscoelastic organic glue [112,141].

6.2.2. Conch (Strombus gigas) shellThe conch shells, with a spiral configuration, have a structure that is quite di!erent

from the abalone nacre. Fig. 69a shows the overall picture of the well known S. gigas (pinkconch) shell. In contrast with the abalone shell, which is characterized by parallel layers oftiles, the structure of the conch consists of three macrolayers which are themselves orga-nized into first-order lamellae, which are in their turn, comprised of second-order lamellae.These are made up of tiles named, in Fig. 69a, third-order lamellae in such a manner thatsuccessive layers are arranged in a tessellated (‘tweed’) pattern. Ballarini et al. [194]described nanoscale components in this structure beyond the third order lamella. Thethree-tiered structure is shown in Fig. 69b. This pattern, called cross-lamellar, is reminis-cent of plywood or crossed-ply composites and has been studied extensively by Heuer andcoworkers [131]. The crossed lamellar microstructure consists of lath-like aragonite crys-tals (99,9% of weight) and a tenuous organic layer (0.1 wt%). The ‘‘plywood’’ structureshown in Fig. 69b [11] consists of three macroscopic layers; the inner (closest to the organ-ism), middle and outer layer, which are of relatively uniform thickness within the lastwhorl. This was further characterized by Hou et al. [153]. Kamat et al. [154] showed thatthe result of this structure is a fracture toughness exceeding that of single crystals of the

Fig. 68. Di!erent models for sliding between tiles; inter-tile layer formed by (a) asperities; (b) organic layer actingas viscoelastic glue; (c) mineral bridges.


pure mineral by two to three orders of magnitude. An interesting analogy with a largedome structure is shown in Fig. 70. The Florence dome, built by the architect Bruneleschi,uses a tessellated array of long bricks which have a dimensional proportion similar to the

Fig. 69. Conch shell; (a) overall view; (b) schematic drawing of the crossed-lamellar structure. Each macroscopiclayer is composed of first-, second- and third-order lamellae (from Menig et al. [11]).

Fig. 70. Tesselated bricks on Brunelleschi’s Duomo (Florence, Italy) and equivalent structure of conch shell.


tiles in conch. This arrangement provides the dome with structural integrity not possiblebefore that time.

These three layers are arranged in a 0"/90"/0" direction. So-called first-order lamellaecompose each macroscopic layer and are oriented ±35–45" relative to each other. In eachfirst-order lamella are long thin laths stacked in parallel known as second-order lamellae.These second-order lamellae in turn consist of single crystal third-order lamellae. Finegrowth twins at an atomic scale layer each third-order lamella [155]. The organic matrixwith its 0.1 wt% has only been observed by TEM as an electron dense layer that envelopseach of the third order lamellae [144]. Kuhn-Spearing et al. [155] measured flexural strength,crack-density evolution andwork of fracture for wet and dry specimens of the S. gigas conchshell. Four-point-bending tests in two di!erent orientations were conducted parallel andperpendicular to the shell axis. They report that the tensile strengths of crossed-lamellarshells are 50% lower than the strongest shell microstructure (nacre). Average apparent flex-ural strengths for dry and wet crossed-lamellar samples in the parallel orientation werefound as 156 ± 22 MPa and 84 ± 49 MPa, respectively. The average apparent flexuralstrength of the perpendicular wet and dry samples was 107 ± 38 MPa. The results ofKuhn-Spearing et al. [155] on the fracture of these shell structures suggest that the mechan-ical advantage is an increased fracture resistance, in addition to a previously observedincreased hardness. The tests revealed a work of fracture of 4 ± 2 J/m2 for dry and13 ± 7 J/m2 for wet samples tested in parallel orientation. These values are much higherthan those reported for nacre (0.4 J/m2 for dry and 1.8 J/m2 for wet samples [133]). Theincreased fracture resistance for wet samples is correlated to a decreased interfacial strengththat results in more extensive cracking pattern. Menig et al. [11] also performed a series ofmechanical tests on the conch shell. Fig. 71 presents theWeibull statistical analysis of conchin (a) quasi-static compression and (b) dynamic compression. In quasi-static compressionthe conch shell exhibited a failure probability of 50% [F(V) = 0.5] at 166 MPa and218 MPa for the perpendicular and parallel direction of loading, respectively. In dynamicloading the 50% failure probabilities of the conch shell are found at 249 MPa and361 MPa perpendicular and parallel to layered structure, respectively.

The fraction of organic material in conch is lower than in abalone: !1 wt%, vs. 5 wt%.The strategy of toughening that has been identified in the conch shell is the delocalizationof crack by distribution of damage [11]. An example of how a crack is deflected by thealternative layers is shown in Fig. 72a. The fracture surface viewed by SEM shows thecross-lamellar structure (Fig. 72b) in a clear fashion. The lines seen in the damaged surfaceof conch shown in Fig. 70 indicate sliding of the individual, tiles. The absence of a clearcrack leads to a significant increase in the fracture energy in comparison with monolithiccalcium carbonate.

However, as with the abalone nacre, the structural hierarchies ranging from nano tomacro are all responsible for the over all mechanical response of the shell. The crackdeflection within the microstructure of tessellated tiles is only part of a larger crack delo-calization mechanism. When the crack reaches the inner macrolayer it can again orientitself into an ‘axial splitting’ configuration (seen in Fig. 72a). The 0"/90"/0" architecturearrests the easy-to-form channel cracks and leads to additional channel cracking. Dueto 45" second-order lamellar interfaces the channel cracks (between first-order interfaces),which eventually penetrate the middle macroscopic layer, are deflected and failure is non-catastrophic. It is this complex layered architecture that is responsible for improved tough-ness over that of nacreous structures [144].


Fractographic observations identify delocalized damage in the form of multiple channelcracks, crack bridging, crack branching, and delamination cracking. This increases thetotal crack area and frictional dissipation. Fig. 73 shows schematically channel- anddelamination cracks in a bend specimen-loading configuration used by Kuhn-Spearinget al. [155]. The many interfaces between aragonite grains in the crossed-lamellar structureprovide a multitude of places for energy dissipation.

Laraia and Heuer [128] performed four-point bending tests with S. gigas shells while theshell interior and exterior surfaces were the loading surfaces and were not machined out.

Fig. 71. Weibull plots of conch shell in (a) quasi-static compression, and (b) dynamic compression (from Meniget al. [11]).


They found flexural strengths of about 100 MPa. With the exterior surface loaded in ten-sion, the failure occurred catastrophically; however, when loaded with the interior surfacein tension this kind of failure did not occur. This confirms the anisotropy of shells withcrossed-lamellar microstructure, which leads to ‘‘graceful failure’’ in some orientations.Another indication for the anisotropy mechanical behavior of crossed-lamellar shellscan be found in Curry and Kohn [156]. They found flexural strength (in three-point bend-ing) of shells of Conus striatus in the range of 70–200 MPa depending on the orientation.

Laraia and Heuer [144] found that the resistance to crack propagation is due to severaltoughening mechanisms simultaneously. These are crack branching (i.e. the microstructureforces the cracks to follow a tortuous path), fiber pullout, microcracking (microcracks fol-low interlamellar boundaries), crack bridging and microstructurally induced crack arrest.

Fig. 72. Fracture patterns in conch shell; (a) crack delocalization shown in polished section; (b) scanning electronmicrograph of fracture surface showing cross lamellar structure (from Lin et al. [10]).


Kamat et al. [157] found that the synergy between tunneling cracks and crack bridging wasthe source of a additional factor of 300 in fracture energy. They also carried out microin-dentation experiments. However, for applied loads from 0.1 to more than 10 kgf theindentations failed to produce radial cracks when applied to polished interior shell sur-faces. The damaged zones were elongated and the crack followed first-order lamellae.

The fracture surfaces are shown in Fig. 74. It seems that the conch is designed for max-imization of energy dissipation regardless of the cost in terms of crack formation. Thisallows the mollusk to survive the attack of a crab or another impact event. The molluskcan hide while repairing its damaged material. This designing strategy is also desirable forarmor, however, not necessarily appropriate for structural composites where lifetime andmaintenance are also issues [154].

6.2.3. Giant clam (Tridacna gigas)The giant clam (T. gigas) can grow its shell to widths greater than 1 m, with weights of

over 340 kg [158]. The large amount of shell material produced has made the giant clam ofinterest in both contemporary, as well as historical context. Moir [159] documented the useof this shell as the raw material for applications such as blades for wood cutting tools inancient and present day Takuu Atoll dwellers of Papua New Guinea. The structure of theshell has a low level of organization in comparison to other shells, yet its sheer mass resultsin a strong overall system. The protective shell consists of two distinct regions, an outerwhite region and an inner translucent region.

A detailed study of the structure of the giant clam shell and the role of that structure onthe mechanical strength of the shell was carried out by Lin et al. [10]. The outer region actsas the animal’s first line of defense against the harsh environment. This region appears tocomprise approximately one third of the shell thickness and is formed from dense struc-tured layers of aragonite needles approximately 1–5 lm in length [159]. Growth bands,which extend perpendicular to the direction of shell growth, are thought to contain a thinorganic matrix, partially separating layers of the crossed lamellar aragonite needles [160].The structure of the outer region of the shell, presented in Fig. 75, somewhat resembles the

Fig. 73. Bend specimen loading configuration, shown relative to the material architecture, with a typical pre-failure cracking pattern (channel and delamination cracks) (from Kuhn-Spearing et al. [155]).


microstructure of the middle macro-layer of conch shell, yet a considerable decrease inorganization is observed. Growth bands form first-order lamellae, separating layers of sec-ond and third-order lamellae perpendicular to the direction of growth. The second-orderlamella is composed of planes, parallel to the growth direction, which separate planes ofneedles (third-order lamella) with alternating orientation. The directions of needles alter-nate between +60" and &60" to the direction of growth for each second-order lamella.

Within the inner region of the shell, the microlayered structure is also observed as con-tinuous planes of growth bands. These layers separate approximately 3–7 lm of inorganicmaterial and span normal to the direction of shell growth. Long single crystals of arago-nite travel along the direction of growth and are not interrupted by growth bands. Thisinner region appears more transparent than the outer region and contains a high concen-tration of flaws traveling along the single columnar crystal interfaces. These flaws, in the

Fig. 74. Fracture surface of S. gigas (a) parallel to growth direction, (b) perpendicular growth direction (from Linet al. [10]).


form of microcracks, travel along the direction of growth facilitating crack propagationalong abutting interfaces of neighboring crystals. Fig. 76 shows an optical micrographof the microcracks along columnar crystal interfaces. The observed growth bands in themicrostructure do not interrupt the growth of single crystals from one band to the next,and thus have a minimal e!ect on crack deflection.

Fig. 75. Schematic representation and SEM image of T. gigas shell outer region (from Lin et al. [10]).

Fig. 76. Optical micrograph of polished cross-sectional specimen of T. gigas shell (inner region), with continuoussingle crystal facilitating crack propagation (from Lin et al. [10]).


Fig. 77a presents the Weibull statistical distribution of giant clam in quasi-static com-pression. Where the conch shell from Section 6.2.2 had a failure probability of 50%[F(V) = 0.5] at 166 MPa and 218 MPa for the perpendicular and parallel direction of load-ing, respectively, the giant clam shell showed 50% failure probability at 87 MPa and123 MPa for loading parallel and perpendicular to layered structure, respectively. Theabalone shell from Section 6.2.1 outperformed both the conch and the giant clam shellsby over twice the compressive strength in quasi-static loading. With failure probabilitiesof 50% being reached at 235 MPa and 540 MPa with loading parallel and perpendicular

Fig. 77. Weibull plots of T. gigas shells in: (a) quasi-static compressive loading, (b) dynamic compressive loading(from Lin et al. [10]).


to layered structure, respectively, the abalone also exhibits the highest di!erence instrength between loading directions, consistent with the level of microstructure anisotropy.

A similar trend in dynamic compression strength is observed with the compressivestrength of abalone approximately twice that of the conch shell, and the conch shell havingapproximately twice the compressive strength of the giant clam shell. Shown in Fig. 77bthe 50% failure probabilities of giant glam in dynamic compression are found at154 MPa and 202 MPa for parallel and perpendicular loading directions, respectively. Thisis far less than both the conch and the abalone shells. It is clear that all three materialsexperience greater compressive strengths in dynamic loading than in quasi-static loading;these results have been listed in Table 8.

The microstructure of the giant clam shell consists of both an inner, translucent brittleregion, with relatively low organization, and an outer white, tougher region, which resem-bles the shell of the S. gigas (conch). The inner region fails at the crystal interfaces seen inFig. 75 through a mechanism of axial splitting. Initial microcracks within this regionextend and coalesce under applied stress, resulting in the failure of the shell samples.

It is important to note that the mechanical strength of the outer solid white region ofthe clam shell is over 10 times that of the inner translucent region. Fig. 78 shows scanningelectron microscopy of the fracture surfaces of the shell in bending (a) perpendicular togrowth bands, and (b) parallel to growth bands; this directional dependency has been fur-ther clarified in Table 9. A cross lamellar structure can be seen in Fig. 78a, in which thehorizontal line marked with an arrow is a growth band extending perpendicular to thefracture surface. The alternating planes of fibrous crystals travel at 30" angles to the planesof the growth bands. Separation of material at the growth band interfaces occurred inshear during bending loading perpendicular to planes of growth interruption. Fig. 78bshows the fracture surface of a sample under tension in bending. Separation occurredacross a single growth band, and second-order lamellae are observed as planes of fiberstraveling perpendicular to the fracture surface and alternating in fiber angles. The surfaceseparated cleanly at a single growth band across the entire sample. These observationsindicate that separation occurs at the growth band interfaces in both loading directions,parallel and perpendicular to the growth direction.

6.3. Shrimp hammer

The mantid shrimps are predatory on hard-shelled animals such as clams, abalones, andcrabs using their limbs as hammers. Although the smashing shrimp makes thousands ofenergetic strikes over months, the hammer is rarely damaged. The composition and struc-tural features of the smashing limbs have been studied by Currey and his co-workers [167].

Table 8Comparison of compressive strengths at 50% failure probability for various shells

Species 50% Failure probability stress (quasi-staticloading)

50% Failure probability stress (dynamicloading)

Perpendicular Parallel Perpendicular Parallel

Conch 166 MPa 218 MPa 249 MPa 361 MPaGiant Clam 123 MPa 87 MPa 202 MPa 154 MPaRed Abalone 540 MPa 235 MPa 735 MPa 548 MPa


Fig. 79a shows a typical mantid shrimp and its smashing action. The smashing limb con-sists of the merus, the propodite, and the dactyl. The dactyl is the part used to strike theprey and is highly mineralized. Fig. 79b is a schematic presentation showing the cross-sec-tion of propodite and dactyl. Both propodite and dactyl show three regions: soft tissue inthe central, a layer of fibrous chitin cuticle in between, and a layer of heavily calcifiedregion on the outside. The dactyl used to smash hard-shelled prey has a thick, heavily

Fig. 78. Fracture surface of T. gigas under bending (a) perpendicular to growth bands, (b) parallel to growthbands (from Lin et al. [10]).


calcified layer, while the propodite has much thinner heavily calcified layer. The microh-ardness measurements (Fig. 79c) indicate that the dactyl becomes much harder towardouter surface. The increase in hardness is associated with the increased mineralizationof the cuticle as well as the replacement of calcium carbonate by calcium phosphate.Fig. 79d shows the relationship between the microhardness and the ratio of phosphorus

Table 9Flexure strength for various shells [10]

Species

Conch 74 MPa 29 MPa –Giant Clam (outer

region)39.9 MPa 79.6 MPa –

Giant Clam (innerregion)

– 7.86 MPa –

Red Abalone – 197 MPa 177 MPa

Fig. 79. (a) The smashing limb and typical smashing action of mantid shrimp, Gonodactylus chiragra. (b) Thecross-section of the propodite and dactyl shows three regions: heavily calcified outer layer, fibrous region, andinner soft tissue. (c) Values for microhardness and values for P:Ca (multiplied by 1000). (d) Relationship betweenmicrohardness and the P:Ca ratio (from currey et al. [167]).


to calcium. There is a strong and linear relationship between the hardness and the P:Caratio. The smashing limb, or dactyl, of the mantid shrimp is a natural composite whichis composed of hard, brittle, highly-calcified outer layer and relatively soft, ductile, fibrousinner layer. The fibrous region between the hard outer layer and soft tissue not onlyabsorbs the kinetic energy but prevents cracks from propagating through the cuticle.The outer layer has a su"cient thickness of heavily calcified cuticle with a significantamount of calcium carbonate replaced by calcium phosphate. The hammer of the mantidshrimp is well designed to break hard objects and is an optimized biological ceramiccomposite.

6.4. Marine worm teeth

It was discovered in 1962 by Lowenstam [168] that the teeth in chitons (mollusk worms)contained iron oxide in the magnetite structure (Fe3O4). This discovery was followed byanother one, by Lichtenegger et al. [169]: the carnivorous marine worm Glycera has teeththat contain a copper mineral atacamite [Cu2(OH)3Cl]. These minerals are contained inmineralized fibrils, as shown in the schematic picture of a tooth (Fig. 80a). These miner-alized fibrils are similar to the ones forming in dentin and bone. Again, we have a compos-ite structure with hard fibers embedded in a softer protein matrix. The degree ofmineralization varies along the tooth and the hardness and the elastic modulus are directlyrelated to the mineralization. Lichtenegger et al. [169] used the Halpin–Tsai equation wellknown in the composites field to calculate the hardness and Young’s modulus upper and

Fig. 80. (a) Schematic model of mineralized fibers in Glycera jaws. (b) Hardness and elastic modulus versusmineral content. Dashed and dotted lines: Halpin–Tsai boundaries (from Lichtenegger et al. [169]).


lower bounds. The upper bound corresponds to loading parallel to fiber direction; thelower bound corresponds to loading perpendicular to it. The calculations as well as exper-imental results are shown in Fig. 80b. The Halpin–Tsai upper and lower bounds are indi-cated by dotted and dashed lines in Fig. 80b.

6.5. Bone

Bone is a ceramic (calcium phosphate, or hydroxyapatite)-polymer (collagen) compos-ite. Bone is the structural component of our body. It also has other functions, but we willconcentrate on the mechanical performance here. There are two principal types of bone:

Fig. 81. (a) Longitudinal section of a femur (from Mann [7, Fig. 2.9, p. 11]). (b) Photograph showing a cross-section of elk antler.


cortical (or compact) and cancellous (or trabecular, or porous). Cortical bone is found inlong bones (femur, tibia, fibula, etc.). Cancellous bone is found in the core of bones and inflat bones.

6.5.1. StructureFig. 81a shows the structure of a long bone. The surface regions consist of cortical

bone; the inside is porous and is called cancellous bone. Fig. 81b is a cross-sectional pic-ture of deer antler. The porosity reduces the strength of the bone and antler, but alsoreduces their weight. They are shaped in such a manner that strength is provided onlywhere it is needed. The porosity of cancellous bone provides interesting mechanical prop-erties. The mechanical strength is determined by the porosity and the manner in which thisporosity is structured. The pores also perform other physiological functions and containthe marrow. Thus, bone is a true multifunctional material.

6.5.2. Elastic propertiesBone is a composite of collagen, hydroxyapatite, and water. Hydroxyapatite is a cal-

cium phosphate with the following composition:

Ca10"PO4#6"OH#2Water corresponds to 15–25 vol% of the bone in mammals. The structure of bone is

only partially understood and is, as shown in Fig. 3 hierarchical. The Young’s modulusof cortical bone varies from 8 to 24 GPa. This is much lower than that of hydroxyapatite,which has a Young’s modulus of approximately 130 GPa and a strength of 100 MPa.Although collagen is not linearly elastic, we can define a tangent modulus; it is approxi-mately 1.25 GPa. The broad variation mentioned earlier is seen clearly. There have beenseveral attempts to model the elastic modulus of bone. They are based on our knowledgeof composites. We have two limiting conditions: when the loading is carried out along thereinforcement direction:

Voigt model:

Eb $ V haEha % V cEc "29#

When it is carried out perpendicular to the reinforcement direction:Reuss model:

1=Eb $ V ha=Eha % V c=Ec "30#

The indices b, ha, and c refer to bone, hydroxyapatite, and collagen, respectively. Inbone, the orientation of the collagen fibers and mineral is di"cult to establish. They arenot all aligned, which adds to the complexity. Taking the values given above and applyingthe Voigt and Reuss equations leads to, for 50 vol% collagen:

Eb "Voigt# $ 50 GPa

Eb "Reuss# $ 4 GPa

This is an unacceptably broad range and more elaborate models, discussed below, areneeded. Fig. 82 shows the Young moduli for a number of bones with mineral fractionsvarying from 0.28 to 0.56. The experimental results are compared with the Voigt andReuss averages. Experimental values [2] (Fig. 82) fall between the two limits set by theReuss and Voigt averages. The hydroxyapatite content of bone varies from animal to ani-


mal, depending on function. Antlers have a low mineral content (!0.3). For instance, anagile animal like a gazelle has bones that have to be highly elastic. Thus, the hydroxyap-atite level is fairly low (around 50% by weight). Collagen provides the elasticity. On theother hand a whale has bones with a much higher mineral content (!80% by weight).An aged professor is somewhere in between. Note that the density of hydroxyapatite isapproximately twice that of collagen (!1 g/cm3).

A more realistic model was proposed by Katz [170]. It takes into account the misorien-tation between the external loading axis and the collagen fibrils. He considered di!erentorientations of collagen fibrils, each one with a fraction fi and angle ui with the loadingaxis. The Young’s modulus is

Eb $EcV c 1& mcmb" #

1& m2c%X

EhaV hafi cos4 ui & mb cos2 ui sin2 ui

& '"31#

The Katz equation is essentially a Voigt model that ascribes a contribution to Eb

decreasing rapidly with misorientation ui because of the fourth power dependence ofthe cosine of ui.

This was the basis of Jager and Fratzl’s [171] model for the elastic modulus, that consid-ers that minerals and collagen can overlap. The mineralized turkey leg tendon is a fascinat-ing material; we have all encountered these long and sti! rods at Thanksgiving dinners anda few of us have wondered why they are so di!erent from chicken bones. These mineralizedtendons (connecting bone to muscles) are ideal specimens for the investigation of thestrength of partially mineralized bone and for the establishment of their structures. The col-lagen fibrils are arranged in a parallel fashion and the degree of mineralization increaseswith the age of the turkey. The minimum degree of mineralization of the turkey leg tendon

Fig. 82. E!ect of mineral volume fraction on Young’s modulus of bones from many animals (reproduced fromCurrey [2, Table 4.3, p. 130]).


is 0.15, which is substantially less than bone. The mineralized turkey tendons enable theunderstanding of how the hydroxyapatite and collagen interact.

The physical model applied by Jager and Fratzl [171] is shown in Fig. 83. The collagenfibrils are arranged in concentric layers. Embedded into them are the bone platelets. Thesemineral crystals have nanoscale size, the thickness being typically on the order of 1 nm, thelength being approximately 60–100 nm. This agrees with the picture shown in Fig. 3. Thepartially mineralized bone can be modeled as a composite in which the reinforcement(hydroxyapatite crystals) is essentially rigid and the continuous collagen matrix carriesthe load. The degree of mineralization, U, is defined as

U $ ld"l% a#"b% d# "32#

where a is the overlap between the crystals, b is the lateral distance between them, and land d are the dimensions of the mineral platelets. All parameters are given in Fig. 83b.

Fig. 83. (a) Schematic drawing showing the 3D arrangement of mineral platelets in a collagen matrix. (b) Thestaggered arrangement of mineral platelets. The dimensions of the mineral l and d, the distances between them aand b, are indicated (reproduced from Jager and Fratzl [171, p. 1739, Fig. 3]).


The elastic modulus is considered as comprised of contributions from four regions: (a)the tensile regions A and B and (b) the shear regions C and D as shown in Fig. 84. TheYoung’s modulus, considering these four contributions, was found to be

E0 $ E=EC $ E1 % E2 % E3 % E4 "33#

where EC is the Young’s modulus of collagen and E1 to E4 are the contributions from re-gions A to D, respectively.

Thus,

EEc

$ d"l% a#ab

% 1% l2a

$ %% c"l& a#"l% a#

4b2% ca"l% a#2b"2b% a#

"34#

Fig. 84. Two adjacent elementary cells in the staggered model showing the regions of tensile (A and B), and shearstresses (C and D) respectively (from Jager and Fratzl [171, p. 1740, Fig. 4]).

Fig. 85. Results for the elastic modulus, E 0, the maximum strain, e0max, and the maximum stress, r0max. (a)

U = 0.42, (b) U = 0.15 (from Jager and Fratzl [171, p. 1742, Figs. 5 and 6]).


The predictions of the Jager–Fratzl crystal model for two values of U (= 0.15, typical ofmineralized turkey tendon, and = 0.42, typical of bone) are shown in Fig. 85b and a,respectively. A typical value of crystal thickness d = 3.5 nm was taken. The line markeds corresponds to the maximum in r 0

max, the maximum elastic normalized to the maximumcollagen stress, (rmax/(rmax)c). The spacing between platelets was varied. It can be seenthat the optimal spacing corresponds to b = 4 nm for bone and b = 14 nm for mineralizedturkey tendon. The predicted values of the normalized Young’s modulus E 0 (= 15 forU = 0.15 and = 150 for U = 0.42) correspond to the experimentally obtained values: 8–15 and 200–400, respectively. Thus, one concludes that the stitching and spacing of min-eral platelets is very important in determining the mechanical properties.

Fig. 86. E!ect of mineral volume fraction on (a) tensile strength and (b) toughness (as measured by area understress–strain curve) of di!erent bones (reproduced from Currey [2, Fig. 4.3, p.132 and Fig. 4.5, p. 135]).


6.5.3. StrengthBoth the strength of bone and its toughness, roughly measured by the area of the stress–

strain curve to failure, are dependent on the degree of mineralization, as evident in Fig. 86.The correlation between toughness and degree of mineralization, which was developed byCurrey [2] from a wide variety of animals, is much better than the one of tensile (3-point

Fig. 87. E!ect of orientation on tensile stress–strain curve of bovine fibrolamellar bone (reproduced from Currey[2, Fig. 3.8, p. 89]); (b) tensile and compressive stress–strain curves for cortical bone in longitudinal and transversedirections (reproduced from Lucas et al. [172, Fig. 17.7, p. 268]); (c) schematic drawing showing plasticmicrobuckling; (d) scanning electron micrograph of horse femur bone after compression test showing buckling(courtesy of R. Kulin and K.S. Vecchio, UC San Diego).


bending) strength, because the latter is also a!ected by orientation and other factors, asshown below. The point on the right-hand side is the whale bulla. Antlers have a lowdegree of mineralization and are on the left-hand side.

The longitudinal mechanical properties (strength and sti!ness) are higher than thetransverse ones. Cortical bone can be considered as orthotropic.

The tensile properties of fibrolamellar bone (compact bone without the Haversiancanals) are di!erent along the three directions as is seen in Fig. 87a. The strength achieved

Fig. 88. Strain-rate dependence of tensile response of cortical bone (a) reproduced from McElhaney [174, Fig. 5,p. 1228]; (b) adapted from Adharapurapu et al. [175, p. 1324].


in bone is therefore higher than both hydroxyapatite (100 MPa) and collagen (!50 MPa),demonstrating the synergistic e!ect of a successful composite. The tensile strength alongthe longitudinal direction is three times as high as the one in the circumferential direction.This is the result of the alignment of the collagen fibrils, mineral component, and bloodvessel cavities along the longitudinal axis. The strength (30 MPa) and fracture strain arelowest in the radial direction. The energy absorbed to fracture (area under the stress straincurve) in the longitudinal direction is approximately 100 times the one in the radial direc-tion. The bone is, in real life, not loaded radially in a significant way and therefore strengthis not needed in that direction.

Fig. 87b provides the tensile and compressive stress–strain curves for cortical bone inlongitudinal and transverse directions [172]. The anisotropy is clearly visible. The boneis stronger in the longitudinal direction. It is also considerable stronger in compressionthan in tension. The compressive response of bone is characterized by a plateau with somesoftening after the elastic limit is reached (lower curves in Fig. 87b). This plateau is pro-duced, at the structural level, by the formation of shear zones which are the result of local-ized buckling of the fibrils. Plastic microbuckling is a well-known phenomenon whencomposites are loaded along the fiber axis and was first described by Evans et al. [173].This is shown in Fig. 87c. The angle of these buckling regions with the compression axisvaries between 30" and 40". The equivalent process for bone is shown in Fig. 87d. Thebuckling parameters, applied to abalone nacre as shown in Section 6.5, can also be appliedas well to bone. The angles as well as shear strain can be obtained from the Argon andBudiansky–Wu equations (Eqs. (22) and (23)).

The mechanical response of bone is also quite strain-rate sensitive. As the velocity ofloading increases, both the elastic modulus and the fracture stress increase. Hence, the sti!-ness increases with strain rate. The stress–strain curves for human bone at di!erent strain-rate are shown in Fig. 88a [174]. Recent results, by Adharapurapu et al. [175] also confirmthat the strain rate dependency of cortical bone as shown in Fig. 88b. The Ramberg–Osgoodequation is commonly used to describe this strain-rate dependence of the elastic modulus

E $ re$ C"_e#d "35#

where r is the stress, e is the strain, _e is the strain rate, and C and d are experimentalparameters. The following are typical values:

Human cranium: C = 15 GPa; d = 0.057.Bovine cortical bone (longitudinal): C = 12 GPa; d = 0.018.

The strain-rate sensitivity of bone is primarily due to the collagen. Polymers have a highstrain-rate sensitivity and thermal softening that are well represented by equations devel-oped by Mooney and Rivlin [74,75], Treloar [176], and Arruda and Boyce [177]. Arrudaand Boyce used the following formulation to describe the strain-rate sensitivity of strength:

sAP $ s_c_c0

$ %m

"36#

where _c is the strain rate, m is the strain-rate sensitivity, sAP is the applied stress, and theother two terms are material parameters. This is of the same nature power law as the Ram-berg–Osgood equation.


6.5.4. Fracture and fracture toughness of boneFig. 89 gives the J-integral (Jc) for a number of biological materials as a function of

elastic modulus [17]. The square of fracture toughness (Kc) can be obtained by multiplyingJc by the Young modulus (Kc = (E Æ Jc)

1/2). The plot shows lines of equal fracture tough-ness, drawn as diagonals. As we move toward the right, the toughness increases. Fig. 89provides a valuable insight into the toughness of biological materials. As seen in Section6.2, shells have toughness much superior to calcite, although the composition is similar.Similarly, bone has a toughness significantly higher than fully dense hydroxyapatite,and antler is slightly tougher than bone.

Table 10 shows the fracture toughness of bovine bone tested by di!erent researchgroups [178,179]. Bone owes part of its toughness to the formation of microcracks aheadof the main crack. These microcracks form a process zone which decreases the stress con-centration ahead of the crack tip. These microcracks tend to initiate in highly mineralizedregions and do not grow to become macrocracks. Rather, they are arrested at internal

Fig. 89. A material property chart for natural materials, plotting toughness against Young’s modulus. Guidelinesidentify materials best able to resist fracture under various loading conditions (from Wegst and Ashby [17, p.2171, Fig. 6]).


obstacles, such as Haversian canals. Hard biological materials fracture and the knowledgethat we have gained in synthetic materials can be extended to them. The quasi-staticfracture toughness of human cortical bone was investigated by Ritchie and co-workers[180]. The key findings are the identification of the principal contributing mechanisms thatwill be seen later in this section. The fracture toughness, KIc, varied in the range:

Table 10Fracture toughness of bone

Type bone Direction KIc (MPa m1/2) Source

Bovine femur Long.a (slow) 3.21 Melvin and Evans [178]Long. (fast) 5.05Tansv. (slow) 5.6Transv. (fast) 7.7

Bovine tibia Long. (very slow) 3.2 Behiri and Bonfield [179]Long. (slow) 2.8Long. (fast) 6.3

a Direction of crack propagation.

Fig. 90. Six modes of fracture in bone (adapted from Hall [181, Figs. 4–6, p. 102]).


2 MPa m1=2 < KIc < 5 MPa m1=2

The fracture and fracture prevention in bone are of extreme importance. We know thatbone strength decreases as porosity increases. This is one of the changes undergone by bonewith aging. There are many fracture morphologies in bone, depending on the loading stres-ses, rate of loading, and condition of bone. Fig. 90 presents some of these modalities [181].

Greenstick fracture: This occurs in young bone, which has a large volume fraction ofcollagen; it can break like a green twig. This zig-zag fracture indicates a high toughness.

Fissured fracture: This corresponds to a longitudinal crack in bone.Comminuted fracture: many fragments are formed. This is typical of a fracture caused

by impact at high velocities. Two factors play key a role. As the velocity of projectile isincreased, its kinetic energy increases. This energy is transferred to the bone. The secondfactor is that at high rates, many cracks are produced simultaneously; they can grow inde-pendently until their surfaces intersect. This is the reason why a glass, when thrown on theground violently, shatters into many small fragments. An additional reason is that thebone becomes sti!er and more brittle as the strain rate is increased. This type of fractureis characteristic of bullet and shrapnel impact.

Transverse fracture: This is a complete fracture approximately normal to the axis of thebone.

Oblique fracture: Complete fracture oblique to the bone axis.Helical fracture: This fracture is caused by torsional stresses. This type of fracture is

known, in the medical community, as spiral. However, this name is not correct, and a helixdescribes the crack trajectory better than a spiral. Tensile stresses are highest along sur-faces making a 45" angle with the torsional stresses.

Gibeling and coworkers [182] studied the fracture toughness in the leg bones (thirdmetacarpal bone) in horses and found that fracture toughness increases with crack length.This behavior is similar to ceramic matrix composites. This increase in fracture toughnesswith crack growth in ceramic matrix composites is indicative of mechanisms of tougheningin the material that are due to the existence of the reinforcing and matrix component.Microcracks in the ceramic phase and crack bridging can produce a decrease in overallstress concentration (crack-tip shielding).

Fig. 91. Crack resistance curve as a function of length for horse bone (from Malik et al. [182, Fig. 3, p. 190]).


When the fracture toughness is dependent of crack size, linear elastic fracture mechan-ics cannot be applied and one has to apply other testing methods, such as the R curve. Inthe case of horse leg bone, it was found that there is debonding along macroscopic lamellarstructures ahead of the crack, leading to crack deflection, crack energy absorption, andtoughening as the crack grows. Fig. 91 shows the increase in KR with crack length. Foran initial crack length of 9.76 mm, the initial value of the toughness is 5 MPa m1/2. Thetoughness increases to 6 MPa m1/2. Therefore, the resistance to fracture has to be evalu-ated according to the R-curve method.

Ritchie and co-workers [180] evaluated the contributions of several mechanisms to thefracture toughness of bone. A couple of mechanisms are shown in Fig. 92 [183]. Fig. 92ashows a crack, ahead of which there is a zone of damaged material consisting of cracksthat are not connected. As bridges form between these cracks, the crack front advances.The bridging by collagen fibers in the wake of the crack is another mechanism. This isshown in Fig. 92b.

Table 11 shows the contribution of these mechanisms. For bone, the most importantmechanism is crack deflection, which contributes over 50% to the toughness. The secondmost important one is the formation of bridges between uncracked ligaments, which con-tributes 1–1.5 MPa m1/2.

Fig. 93 shows the critical stress intensity factor for human bone with di!erent ages as afunction of the crack size [184]. For young subjects (34–41 years), K increases considerablywith crack length, a. This is clear R-curve behavior in bones, i.e., increase in toughness asthe crack length is increased and is analogous to the behavior observed by Gibeling et al.[182] and shown in Fig. 91. Fig. 93 also shows that the initial fracture toughness decreasedwith age. However, and more importantly, the increase in toughness with increasing cracklength decreases with age, evidencing that the principal extrinsic toughening mechanismscease to operate in old bone. Hence, a crack, once initiated, is more likely to stop in ayoung bone than in an old one.

Longitudinal toughness is lower than transverse toughness. This occurs because thecrack propagates more readily along the fibrils. The results in Table 10 also show thatthe toughness increases as the strain rate is increased. This increase in toughness withstrain rate is a desirable property, because bones often break by impact loading. Thereis no significant di!erence between the femur and the tibia.

In determining the fracture toughness, the minimum dimensions of the specimen arecritical. For plane-strain conditions under which KIc tests are valid, the minimum thick-ness is

B P 2:5KIc

ry

$ %"37#

For bone, this value is on the order of a few millimeters. Hence, specimens can be ratherthin. However, the increase in K with crack length, a, requires that a GIc analysis be used.

Bone fatigue is well documented. This phenomenon is commonly – and incorrectly –known in the medical community as ‘stress fracture.’ Repetitive loading above a thresholdoften generates this type of damage in athletes. It is attributed to the formation of micro-cracks which develop throughout the bone. These microcracks do not grow because of theinternal barriers posed by the Haversian system. Fig. 94 shows the S–N curves for a num-ber of bones [2]. This is very similar to metal fatigue.


Fig. 92. (a) Schematic of discrete damage that has evolved into a single dominant crack tip damage zone. (b) Anoptical micrograph of a crack in human cortical bone. Note the formation of daughter cracks and correspondinguncracked ligaments. Bridging by collagen fibrils in the wake of a crack in human cortical bone (from Yang et al.[183]).


6.6. Teeth

6.6.1. Structure and propertiesTeeth are comprised of an internal region called dentin and an external enamel layer as

shown in Fig. 95a. The structure of the tooth is designed to provide an external layer thatis hard and an internal core (dentin) that is tougher. The hardness of the enamel layer isdue to a high degree of mineralization. Enamel does not contain collagen. It is comprisedof hydroxyapatite rods woven into a fabric-like composite. These rods have a diameter ofapproximately 5 lm, as shown in Fig. 95b [185]. Dentine, on the other hand, is more akinto bone. It contains 30 vol% collagen and 25 vol% water, the remainder being hydroxyap-atite. One of the major features of dentin is the tubules, which have a diameter of about1 lm. They are surrounded by hydroxyapatite crystals (!0.5–1 lm diameter) arranged in arandom fashion. These tubular units are, on their turn, embedded in a composite consist-ing of a collagen matrix reinforced with HAP. This is called the intertubular region. Thesefeatures are shown in Fig. 95c [186].

Table 11Contributions to fracture toughness of bone from di!erent mechanisms (from Nalla et al. [180])

Mechanism Contribution to fracture toughness, KIc (MPa m1/2)

Uncracked ligament bridging 1–1.5Crack deflection 3Collagen-fibril bridging 0.1Constrained microcracking 0.05

Total 2–5

Fig. 93. Resistance-curves for stable ex vivo crack extension in human cortical bone. Note the linearrly rising R-curve behavior (from Nalla et al. [184, Fig. 4]).


Fig. 94. Stress–number of cycles (SN) curves for a number of bones loaded under di!erent conditions(reproduced from Currey [2, Fig. 2.15, p. 52]).

Fig. 95. Hierarchical structure of tooth. (a) Schematic drawing showing enamel, dentin–enamel junction, dentin,and pulp; (b) scanning electron micrograph of mouse tooth shows an etched image of mature enamel where theenamel rods weave past one another (from Snead et al. [185, p. 1292 Fig. 2b]); (c) scanning electron micrograph ofdentin (from Imbeni et al. [186, p. 6, Fig. 6b]); (d) AFM image of a collagen fiber (from Nalla et al. [184, p. 1252,Fig. 10a]).


Table 12 shows the hardness and fracture toughness of tooth [187,188] (the latterobtained from cracks at the extremities of indentation through the Evans–Charles [173]technique). The toughness of enamel is lower than that of the dentin whereas the converse

Table 12Mechanical properties of teeth (from Imbeni et al. [187] and Nalla et al. [188])

Enamel Dentin

Fracture toughness, KIc (MPa m1/2) 0.7–1.3 1–2Hardness (GPa) 4 0.5rUTS (MPa) 70–80Young’s modulus, E (GPa) 60 Perpendicular to tubules: 5–6

Parallel to tubules: 13–17

Fig. 96. (a) Typical profiles of the Vickers hardness and indentation toughness across the dentin–enamel junction(DEJ) (from Imbeni et al. [187, p. 229, Fig. 1]), (b) scanning electron micrograph showing that cracks from theenamel are arrested after propagating into the dentin (from Imbeni et al. [187, p. 231, Fig. 4a]).


is the case for the hardness. The high hardness of enamel is indeed significant: it is thehardest material in vertebrates. However, in contrast with bone, which has a vascularstructure and can undergo self-repair and remodeling, both enamel and dentin are static,never repair, and cannot remodel. The changes in toughness and in hardness across thedentine–enamel junction (DEJ) are shown in Fig. 96a.

Fig. 96b shows a crack initiated in enamel and with a trajectory perpendicular to thedentin-to-enamel junction (DEJ). Imbeni et al. [187] observed that the interface neverdebonds. Rather, the crack penetrates it, travels a short distance (!10 lm) into dentin,and subsequently stops. Fig. 96b shows how uncracked ligaments arrest the crack.

Fig. 97. Macroscopic applied compressive stress versus strain for deciduous bovine dentin. Synchrotron X-raydi!raction rings shown in top left corner (from Deymier et al. [190]).

Fig. 98. Scanning electron micrograph of the typical microstructure of elephant tusk dentin (from Nalla et al.[188, p. 3953, Fig. 1a]).


Fig. 97 is an in situ synchrotron transmission di!raction measurement of deciduousbovine dentin done under an external load [190]. The applied stress on the specimen pro-duces an elastic strain in the HaP which is determined by measuring deformation of dif-fraction rings (shown in insert). The slope is 24 GPa, much less than the modulus of120 GPa for pure HaP, as expected since the porosity and collagen also present in thetooth but are not load-bearing. Thus, a considerable fraction of the deformation is takenup by the collagen.

6.6.2. Growth and hierarchical structure of elephant tuskThe structure of dentin of elephant tusk is shown in Fig. 98. The tubules are seen as

oval features. The insert in the figure shows the tubules and collagen fibers radiating awayfrom them. There is a di!erence between elephant tusk and human tooth dentin. In theelephant tusk, the tubules are more elliptical and there is an almost absence of peritubular

Fig. 99. Scanning electron micrographs of typical crack paths for the nominally ‘‘anti-plane parallel’’ orientationin the context of crack-microstructure interactions. The white arrows indicate in (a) uncracked ligament bridging,and in (b) microcracks in the vicinity of the crack (from Nalla et al. [188, p. 3957, Fig. 9]).


dentin. The presence of tubules confers a considerable degree of anisotropy to the struc-ture. Fig. 99 shows two mechanisms of toughening operating when the crack is runningin the ‘‘anti-parallel’’ direction to the tubules. Uncracked ligaments are seen and markedby arrows in Fig. 99a; microcracks in the vicinity of the cracks are seen in Fig. 99b.

Fig. 100 shows in schematic fashion the four principal toughening mechanisms operat-ing in dentin. The structure is fairly similar to bone, except that dentin is simpler. Themechanical properties in general and toughness in particular are quite anisotropic due tothe presence of the tubules. The Young’s modulus parallel to the tubules is !13 GPa,whereas it is !5–6 GPa perpendicular to the tubules. Similarly, the fracture toughness is!2.5 MPa m1/2 parallel to the tubules and !1.6 MPa m1/2 perpendicular to the tubules.

The four principal toughening mechanisms are seen schematically in Fig. 100. Thesemechanisms are akin to the ones in complex materials. Deflection (Fig. 100a) is causedby barriers which change the path of the crack. Deflection increases toughness by provid-ing the initial barriers and by changing the crack angle from the applied stress from theoptimum 90" condition. Crack bridging can be provided by the collagen fibers, which pro-vides crack-tip shielding (Fig. 100b). It can also be provided by the linkage of the principalcracks with microcracks ahead of the tip, providing uncracked ligaments (Fig. 100c).Microcracking is the damage that is initiated ahead of the crack and forms a process zonewith dilatation which tends to ‘‘close’’ the crack (Fig. 100d). This mechanism has also beenidentified in bone. Contributions of four di!erent toughening mechanisms to KIc in dentinare concluded in Table 13.

Fig. 100. Schematic illustrations of some possible toughening mechanisms in dentin: (a) crack deflection, (b)crack bridging (by collagen fibers), (c) uncracked ligament bridging, and (d) microcracking (from Nalla et al. [188,p. 3959, Fig. 12]).

Table 13Contributions of di!erent toughening mechanisms to KIc in dentin (from Nalla et al. [192])

Mechanism Parallel to tubules Perpendicular to tubules

Crack deflection !1.5 !1Microcracking 0.3 0.25Uncracked Ligament bridging 0.4 0.1Collagen bridging 0.1

Total !2.5 !1.6


The increase in K with crack extension, seen in Section 6.5 for bone, is also observed indentin. This is a direct consequence of the extrinsic toughening due to the formation of aprocess zone behind the crack front (crack wake). Fig. 101 shows this response [191]. Thedi!erent curves apply to specimens with di!erent age, but the trend is clear. Anotherobservation is that dentin hydrated in a standardized saline solution (HBSS) has a highertoughness. Nalla et al. [192] also discovered that dentin toughness increased in alcohol, anauspicious news for hard drinkers.

6.7. Nano-scale e!ects in biological materials

The spatial frontier of Materials Science has for a long time resided at the nanometerscale. The atomic/molecular interactions dictate the structure and properties. This e!ectmanifests itself significantly, as the scale is reduced, for the three classes of syntheticmaterials:

(a) Metals: The grain size has a significant e!ect on strength, and the Hall–Petch equa-tion is widely accepted to determine this dependency. However, it predicts an infinitestrength at infinitely small grain sizes, and therefore it breaks down in the nanometerregime. Indeed, the strength reaches a plateau (and may dip lightly) at grain sizesbelow 50 nm.

(b) Polymers: Polymeric fibers with outstanding mechanical strength can be produced.This strength, which cannot be even approached for bulk materials, is achieved ifall molecular chains are aligned, well cross-linked, and long.

(c) Ceramics: Brittle materials have the strength limited by the critical stress at whichcracks propagate. To a first approximation, this is

Fig. 101. KR resistance-curves for hydrated and dehydrated dentin. Note the significantly higher initial increasein toughness with crack extension for hydrated dentin (from Kruzic et al. [191, p. 5207, Fig. 1b]).


rM $ KIc******pa

p "38#

As the particle size is reduced, so is the maximum flaw size. Thus, there is a minimum flawsize at which the stress required tomake it grow is higher than the theoretical tensile strength.

Gao et al. [193] and Gao and Ji [149] proposed a conceptual framework that explainsthe lowest scale of the structural elements in hard biological materials (bone, teeth, and

Fig. 102. (a) Schematic of mineral platelet with a surface crack (Gri"th analysis); (b) comparison of the fracturestrength of a cracked mineral platelet calculated from the Gri"th criterion with that of a perfect crystal (fromGao et al. [193]). (c) Fracture stress as a function of crack length, 2a (from Meyers et al. [141]).


shells). They applied Gri"th’s criterion to the mineral components of hard biologicalmaterials:

rf $ aEch

$ %1=2

"39#

where c is the surface energy, a is a proportionality constant, and h is the thickness of themineral. They defined a parameter w

w $******cEh

r"40#

For the thumbnail crack shown in Fig. 102a, the value of a is***p

p. The theoretical

stress, rth, has been defined, according to the Orowan criterion, for crystallinematerials, as

rth ) En

2p < n < 30"41#

The analysis predicts a limiting value of h (or a) for which the strength is no longer size-dependent

h+ ) a2cEr2th

$ a2ncE

"42#

This critical value was calculated for bone. A value of about 30 nm was obtained. This isthe approximate size of the ceramic tablets. The critical value of W, W*, is marked inFig. 102b.

Meyers et al. [141] used a similar approach (Section 6.2.1) and obtained, for abalone,the result shown in Fig. 102c. This is quite di!erent from the plate thickness,500 nm = 0.5 lm. The abalone shell has nanoscale components, and they are the mineralbridges connecting layers of tiles. Fig. 67 shows an SEM and Fig. 103 is a schematic illus-tration of these bridges, which have a diameter of !50 nm, in agreement with the analysispresented here.

Fig. 103. Schematic drawing showing the nano-sized mineral bridges connecting layers of aragonite tiles.


(d) Soft biological materials

The long polymeric chains that comprise polypeptides are akin to the synthetic poly-mers. In biological systems, they exist in an aqueous environment. Proteins are comprised,at the elemental level, of –C–C–N– chains. These bonds are covalent and of a high order.The configurations of molecules (e.g. folding) and bonding between neighboring moleculesare often accomplished by hydrogen bonding, which is much weaker. Thus, one wouldexpect a high strength, at the individual molecule level, for proteins. Experiments withAFM are enabling the establishment of the mechanical response of individual molecules,as discussed in Section 8.5. Fig. 104 shows a force–displacement curve obtained by AFMfrom the extension of an individual protein. The sequence of peaks followed by load dropsis indicative of the sequential unfolding of the protein chain. It is possible to convert theload into a stress by assigning a cross-sectional diameter to the molecule. This is taken veryconservatively as 1.5 nm (the diameter of a collagen molecule), to a first approximation.The last peak corresponds to the extension of the fully unfolded protein and leads to fail-ure. The stress is given by

r $ 800, 10&12

1:76, 10&18 $ 454 MPa

Thus, at the nanolevel the protein chains are very strong. The much lower tensile strengthsobtained at the meso level are due to weak links that are introduced between molecularchains, microfibrils, fibrils, and fibers. There are a few exceptions, such as the strengthin fibers from plant, which is 300–400 MPa (e.g., the curaua fibers from Brazil, that areused in composites and have a tensile strength of !500 MPa [189]) and silk, with a strengthon the order of 1 GPa.

Fig. 104. Force vs. displacement curve for protein by AFM for protein. Successive load drops correspond tounfolding of molecular chains by breaking secondary bonds (reproduced from Fisher et al. [274, Fig. 1c]).


6.8. Multi-scale e!ects

Although nanoscale e!ects definitely play a role in the strength of shells, bone, andother biological materials, they by no way determine their toughness, which is establishedby a hierarchy of mechanisms. Hence, the estimate of collagen strength based on a singlemolecule (AFM) gives an ultimate strength around 450 MPa, while the strength in the toeregion of tendon varies between 10 and 20 MPa. The breaking stress after considerablenon-recoverable deformation is !50 MPa. Cross-linking of the collagen molecules by arti-ficial means can increase the strength to !80 MPa.

Failure in larger specimens occurs by a cascade of e!ects that is better understood if welook at the schematic of Fig. 18. There exist permanent deformation/partial failure eventsat the di!erent hierarchical levels: nano, micro, meso, and structural. Separation of themicrofibrils, fibrils, fibers, and fascicles, can produce permanent stretching, and this indeedoccurs in the linear portion of the stress–strain curve, beyond the toe portion. Similarly,

Fig. 105. (a) Crack deflection by middle macrolayer in conch (SEM taken after quasi-static compression testing)(loading direction indicated). (b) Multiple channel cracking and extensive microcracking in outer macrolayer ofconch (from Menig [195]).


bone has nanoscale deformation events described by Fratzl et al. [171]. However, it alsohas events which occur at a considerably larger length scale: the crack bridging phenom-enon, so e!ective in contributing to its toughness (see Section 7.3) operates at the microm-eter scale. Nalla et al. [188] measured the dimensions of the bridging zone in dentin; it wason the order of 50–300 lm. In the fracture of crab exoskeleton, the vent holes and tubulesplay a key role. Their spacing is !2 lm.

The failure of shells is a classic example of multiscale strengthening. In the case of S.gigas, the macrolayers are powerful crack deflectors. Indeed, Fig. 105a shows a crack thatstarted in the inside and is deflected by the interface between the inner and middle macro-layer. This was pointed out by Ballarini et al. [194], who showed that the toughness of boneand S. gigas was accomplished by the hierarchy of barriers, the most important being thearrest of cracks at macrolayer interfaces. The first-order lamellae (see Fig. 105a) act asbridges, closing the cracks. This crack-bridging mechanism operates at the millimeter scale.

The same e!ect contributes to the toughness of abalone shells. The mesolayers, 0.3 mmapart, are separated by organic layers, as discussed in Section 6.1. The cracks are arrestedand deflected at these interfaces. Ballarini et al. [194] argue that the Aveston–Cooper–Kelly limit [196] estimates the length of the bridging zone and the amount of crack growthrequired to reach the ACK limit.

In conclusion, it can be said that the hierarchical structure of biological materials, start-ing at the nanometer level and continuing up to the structural dimensions, is key to thedetermination of the mechanical response. In this context, statistical models akin to theone developed by Bazant and Pang [197,198] for quasi-brittle materials have to be devel-oped. They propose a cumulative density function of strength of a representative volumeelement (RVE) which obeys a Maxwell–Boltzmann relationship, then connect these vol-umes in series and parallel, constructing new distribution functions at a larger space scale.These couplings between RVEs lead to a macroscopic Weibull distribution such as thatone that is observed in abalone and conch (Section 6.2).

7. Biological polymers and polymer composites

The term used by Ashby and Wegst [17], biological polymers, describes the soft tissuesfound in biological systems. Biological polymers can be unidirectional, such as in tendons,two-dimensional, such as in membranes (arteries, heart pericardium, skin), or tri-dimensional.

Fibers are strong in tension but cannot resist compression without buckling and kink-ing. Thus, these fibers are most often used in tension. According to Jeronimidis [199], nat-ure provides compressive strength by

(a) Inserting mineral elements and in this manner creating ceramic composites.(b) Increasing the cross-linking between the fibers and between fiber and matrix to gen-

erate sti!ness.(c) Pre-stressing fibers in tension via an internal pressure. This is the case for skids,

where rigidity of the wall is provided by an internal water pressure that is higher thanthe external one.

(d) Pre-stressing parts of the structure so that some parts are in tension while others arein compression. For example in trees the periphery of the trunk is in tension whilethe core is under compression.


7.1. Ligaments

The function of a ligament is to connect bone to another bone. Tendon connects bone tomuscle. The hierarchical structure of ligament is similar to that of tendon and is based oncollagen fibers. The mechanical behavior of tendon and ligament are similar. Ligamentumnuchae is almost pure elastin and has remarkable elastic properties [27] as will be shown inSection 8.1. Fig. 106a shows the stress–strain curve of ligamentum flavum (ligament betweenlumbar vertebrae) from pig [200]. The ligament has a high ductility and is able to transmitthe stress until maximum stress. Sikoryn and Hukins [200] obtained a maximum stress of2.6 MPa at a low strain rate and of 3.0 MPa at a high strain rate. The ligament strengthseems to be independent of the strain rate. A small strain rate e!ect has been observed at

Fig. 106. Stress–strain curve of ligament from (a) pig (Ligamentum Flavum) (reproduced from Sikoryn andHukins [200]), (b) human (Inferior Glenohumeral ligament) (reproduced from Bigliana et al. [204]).


the tendon of horse [201]. Nachemson and Evans [202] reported that the maximum stressfor human ligamentum flavum had a value 4.4 ± 3.6 MPa. Although the maximum stressfor ligamentum flavum in pigs and humans is on the same order, the strain at maximumstress is not. The maximum stress and strain decreases significantly with age for humans.For young subjects (13 years old), the maximum stress was 10 MPa, decreasing to2 MPa for old subjects (79 years old). The strain at maximum stress is about 2 for pig lig-amentum flavum, as shown in Fig. 106a. For human ligamentum flavum, the strain values arelower (0.5 ± 0.2). It should be mentioned that Chazal et al. [203] reported a much highermaximum stress of 15 ± 5 MPa and much lower strain at maximum stress of 0.21 ± 0.04.

Fig. 106b shows the stress–strain curves for the inferior glenohumeral ligament (fromshoulders) from human [204]. Two di!erent failure mechanisms were observed: the abruptfailure which occurs at the bone-ligament interface (solid line), and the step-like failurewhich occurs within ligaments (dashed line) [204–206]. Fig. 107 shows the fracture surfaceof ligamentum flavum [200]. The ligament failed at the bone-ligament interface due to thedi"culty of connecting flexible ligament to the sti!er bone. B corresponds to the bone,while L is the ligamentum flavum. The arrows indicate interface between tissues.

7.2. Silk

Silk is composed of two proteins: fibroin (tough strands) and sericin (gummy glue).Fig. 108 shows silk (a) with and (b) without the sericin layer. The mechanical properties(strength and maximum elongation) can vary widely, depending of the applicationintended by the animal. For instance, spiders produce two types of silk. The first is thedragline, used in the radial components of the web. This is the structural component,and has high tensile strength (0.6–1.1 GPa) and a strain at failure of about 6%. The tan-gential components, called spiral, are intended to capture prey, and are ‘‘soft’’ and‘‘sticky.’’ The strain at failure can exceed 16 (or 1600%).

Fig. 107. Fracture surface of ligamentum flavum after tension; B: Bone, L: ligamentum flavum (from Sikorynand Huskins [200]).


The silks produced by orb-web-spinning spiders exhibit mechanical properties that aresuperior to almost all natural and man-made materials. Although orb-webs evolved over180 million years ago [207,208] the investigation of the physical structure and properties ofspider’s silk only began in the late 1970s, starting with Denny et al. [209]. Since then themechanical properties of various spider silks have been well described by Kaplan et al.

Fig. 108. SEM micrograph of B. mori silk fibers (a) with and (b) without the gum-like sericin proteins (fromAltman et al. [217]).

Table 14Tensile mechanical properties of spider silks and other materials

Material Sti!ness(GPa)

Strength(GPa)

Extensibility Toughness(MJ m&3)

Hysteresis(%)

Source

Nature fibersAraneus MA silk 10 1.1 0.27 160 65 [213]Araneus viscid silk 0.003 0.5 2.7 150 65 [213]Nephila clavipes silk 11–13 0.88–0.97 0.17–0.18 [214]Bombyx mori cocoon

silk7 0.6 0.18 70 [213]

B. mori silk (w/sericin)

5–12 0.5 0.19 [215]

B. mori silk (w/osericin)

15–17 0.61–0.69 0.4–0.16 [215]

B. mori silk 10 0.74 0.2 [214]Rat-tail collagen 0.002–0.05 0.0009–

0.00740.24–0.68 [216]

Rat-tail collagen X-linked

0.4–0.8 0.047–0.072 0.12–0.16 [216]

Tendon collagen 1.5 0.15 0.12 7.5 7 [213]Bone 20 0.16 0.03 4 [213]Wool, 100%RH 0.5 0.2 0.5 60 [213]Elastin 0.001 0.002 1.5 2 10 [213]Resilin 0.002 0.003 1.9 4 6 [213]Synthetic materialsSynthetic rubber 0.001 0.05 8.5 100 [213]Nylon fiber 5 0.95 0.18 80 [213]Kevlar 49 fiber 130 3.6 0.027 50 [213]Carbon fiber 300 4 0.013 25 [213]High-tensile steel 200 1.5 0.008 6 [213]


[210], Gosline et al. [211], Vollrath et al. [212], and others. The properties of Araneus dia-dematus and Bombyx mori silk in comparison to various other materials are listed in Table14 [213–216]. The removal of sericin increases the strength of the silk.

Spiders are capable of producing a variety of silks, each with distinct functions andmechanical characteristics. The two most studied are

(a) the support, or safety dragline silks, which create the spokes and frame of a web aswell as the lines from which a spider hangs, and

(b) the viscid silks which are used as the prey catching spirals of a web.

Support and dragline silk is spun from the major ampullate (MA) gland of the spiderand is often referred to as the MA silk. Because of its function, MA silk is much sti!er andstronger then the viscid silk fibers which compose the spirals of the web. It can have anelastic modulus on the order of 10 GPa, and a maximum strength of over 1 GPa [210–212]. On the other hand, viscid silk exhibits remarkable extensibility, withstanding up to500% strain before failure in some species [212]. Its elastic modulus is over three ordersof magnitude lower then MA silk yet both have surprisingly similar and incredible tough-ness. The stress–strain curves of both silks are presented in Fig. 109 [213]; a dramatic dif-ference in properties can be seen.

It seems intuitive that the function of the web is to absorb the kinetic energy of a flyinginsect then relax without an elastic recoil that could reject a prey from its entanglement[218]. The microstructure of the MA silk provides a support framework which is able toproduce the required viscoelastic response. It can be thought of as a semi-crystalline mate-rial, with an amorphous region composed of disordered protein chains connected to pro-tein crystals [20,213,219]. These crystals form from layers of anti-parallel amino acidsequences which are known as b-pleated sheets. Fig. 110 provides an illustration of themicrostructure consisting of amorphous proteins crosslinked through crystalline blocks.The silk is spun from multiple fibers of this semi-crystalline material.

The combination of a hard crystalline region and an elastic amorphous region results ina viscoelastic material with a notable strain-rate sensitivity. As shown in Fig. 111,

Fig. 109. Stress–strain curves for MA glad silk and viscid silks from the spider A. diadematus (from Gosline et al.[213]).


increased strain rates result in increased yield stress, tensile strength, and breaking strain[220]. High strain rates reflect the natural condition under which the material is loaded, i.e.

Fig. 110. Schematic representation of the hierarchical microstructure of spider silk (adapted from Elices [30]).

Fig. 111. Strain rate dependence of MA dragline silk (from Elices et al. [220]).


the impact of a fast moving insect. When the material is loaded past its yield stress a regionof strain hardening is observed [221]. The plot in Fig. 112 shows this strain hardeningregion under which most of the energy absorption occurs. This may be due to the rear-rangement of the b-pleated sheet blocks in the amorphous network. The di!erent curvesrepresent di!erent specimens; the figure also illustrates the variability between di!erentspecimens, a characteristic of biological materials.

7.3. Arthropod exoskeletons

Arthropods are the largest phylum of animals including the trilobites, chelicerates (spi-ders, mites, and scorpions), mariapods (millipedes and centipedes), hexapods (insects), andcrustaceans (crabs, shrimps, lobsters, and others). All arthropods are covered by a rigidexoskeleton, which is periodically shed as the animal grows. The arthropod exoskeletonis multifunctional: it not only supports the body, resists mechanical loads, but also pro-vides environmental protection and resistance to desiccation [3,222–224].

The three main components of exoskeleton are chitin, a polysaccharide, structural pro-teins, and inorganic minerals, typically calcium carbonate. In the crustacean species, theexoskeleton shows a high degree of mineralization. However, calcium carbonate is absentin the exoskeletons of insects.

The exoskeleton is a multi-layered structure that can be observed under optical micro-scope, sometimes even by naked eye. The outermost layer is the epicuticle, a thin, waxylayer which is the main waterproofing barrier. Beneath the epicuticle is the procuticle,the main structural part which is primarily designed to resist mechanical loads. The proc-uticle is further divided into two parts, an exocuticle and an endocuticle. The mesostruc-ture of the lobster exoskeleton is shown in Fig. 113a. The exocuticle (outer layer) and

Fig. 112. Strain hardening in MA dragline spider silk (from Garrido et al. [221]).


endocuticle (inner layer) are similar in structure and composition. The di!erence betweenexocuticle and endocuticle is that the exocuticle is stacked more densely while the endoc-uticle is sparsely stacked. The spacing between layers varies from species to species. Gen-erally, the layer spacing in the endocuticle is about three times thicker than that in theexocuticle.

The most characteristic feature of arthropod exoskeletons is their well-defined hierar-chical organization which reveals di!erent structural levels as shown in Fig. 5. At themolecular level is the polysaccharide chitin. Several chitin molecules arrange in an anti-parallel fashion forming a-chitin crystals. The next structure level consists of 18–25 of suchmolecules, wrapped by proteins, forming nanofibrils of about 2–5 nm in diameter andabout 300 nm in length. These nanofibrils further assemble into bundles of fibers of about50–300 nm in diameter. The fibers then arrange parallel to each other and form horizontalplanes. These planes are stacked in a helicoid fashion, creating a twisted plywood or Bouli-gand structure [46,47,225–227]. A stack of layers that have completed a 180" rotation isreferred to as Bouligand or twisted plywood layer, which further forms the exocuticleand endocuticle. The Bouligand (helical stacking) arrangement provides structuralstrength that is in-plane isotropic (plane XY) in spite of the anisotropic nature of the

Fig. 113. (a) A through-thickness SEM micrograph showing that the exocuticle has higher stacking density thanthe endocuticle (from Raabe et al. [236, p. 144, Fig. 2]). (b) The hardness and the reduced sti!ness through thethickness of the lobster exoskeleton (from Raabe et al. [235, p. 4284, Fig. 2]).


individual fiber bundles. In crustaceans, the minerals are mostly in the form of crystallineCaCO3, deposited within the chitin–protein matrix [7,31,228,229]. The highly mineralizedBouligand arrangement provides strength in the in-plane (or in-surface) direction and canbe considered as the hard or brittle component. The flat fracture surface in Fig. 114 showsclear evidence of the brittle structure.

In the vertical direction (Z-direction) as shown in Fig. 115, there are well-developed,high density pore canals (spacing between canals is !2 lm) containing tubules penetratingthrough the exoskeleton, as shown in Fig. 115a. These tubules are hollow and have a flat-tened configuration (!2–3 lm wide) that twists in a helical fashion. They play an impor-tant role not only in the transport of ions during the mineralization of the new exoskeletonafter the animals molt, but also in the enhancement of mechanical properties in the Z-direction. These tubules are organic materials and can be considered as soft or ductilecomponent which stitch the fibrous layers together and provide the toughness to the struc-ture. A region where separation was initiated by tensile tractions is shown in Fig. 115a.The tubules are stretched and fail in a ductile mode. The neck cross-section is reducedto a small fraction of the original thickness. Fig. 115b shows the top view of the fracturesurface (XY plane); the tubules are the lighter segments protruding. Many of them arecurled, evidence of their softness and ductility. It is thought that this ductile componenthelps to ‘stitch’ together the brittle bundles arranged in the Bouligand pattern and pro-vides the toughness to the structure. It also plays undoubtedly a role in keeping the exo-skeleton in place even when it is fractured, allowing for self-healing. These aspects wereinvestigated by Chen et al. [230].

The mechanical properties of crustacean exoskeletons (mud crab, Scylla serrata and theprawn, Penaeus mondon) were first investigated by Hepburn and Jo!e [231,232], followedby Raabe and coworkers (American lobster, Homarus americanus) [233–239] and Chenet al. [230] (sheep crab, Loxorhynchun grandis and Dungeness crab, Cancer magister).

Fig. 114. SEM micrograph of fracture surface showing the twisted plywood (Bouligand) structure of crabexoskeleton (from Chen et al. [230]).


The tensile stress–strain curves for various exoskeletons are shown in Fig. 116. The resultsfrom Hepburn and Jo!e [231] show a unique discontinuity (load drop) in the low strainregion. They suggested that this discontinuity is associated with the brittle failure of themineral phase. When exoskeleton specimens are stretched, brittle failure of the mineralphase occurs at a low strain, leaving the chitin and protein phases to bear the load. Table15 shows the mechanical properties of crustacean exoskeletons [230–232]. The presence ofwater plays an important role in mechanical properties as shown in Fig. 116. The driedexoskeleton material is rigid and brittle compared to that in the hydrated state.

Melnick et al. [240] studied the hardness and toughness of exoskeleton of the stonecrab, Menippe mercenaria, which exhibits a dark color (ranging from amber to black)on tips of chelae and walking legs. The dark material was much harder and tougherthan the light-colored material from the same crab chela (Table 16). Scanning electron

Fig. 115. SEM micrographs of ductile fracture surface show the tubules in the Z-direction in crab exoskeleton;(a) side view showing the necked tubules; (b) top view showing fractured tubules in tensile extension (from Chenet al. [230]).


micrographs (Fig. 117) showed that the dark exoskeleton material has lower level ofporosity, and this may relate to the tanning e!ect. It may also be more highly mineralized.

Raabe and co-workers extensively studied the structure and mechanical properties ofthe exoskeleton of American lobster, Homarus americanus [233–239]. They observed theunique honeycomb-type arrangement of the chitin–protein fibers surrounding pore canals,as shown in the Fig. 118. The honeycomb structure of lobster is quite stable after chemicaland heat treatments, and could be made suitable for medical applications, for example,tissue engineering [239]. The through-thickness mechanical properties of American lobster

Fig. 116. Tensile stress–strain curves for crustacean exoskeletons.

Table 15Mechanical properties of crustacean exoskeletons

UTS (MPa) Young’s modulus (MPa) Fracture strain (%) Source

Sheep crab Wet 29.8 ± 7.2 467 ± 92 6.9 ± 1.8 [230]Loxorhynchus grandis Dry 12.5 ± 2.3 735 ± 65 1.7 ± 0.3Mud crab Wet 30.1 ± 5.0 481 ± 75 6.2 [231]Scylla serrata Dry 23.0 ± 3.8 640 ± 89 3.9Prawn Wet 28.0 ± 3.8 549 ± 48 6.9 [232]Penaeus mondon Dry 29.5 ± 4.1 682 ± 110 4.9

Table 16Mechanical properties of stone crab, Menippe mercenaria [240]

Hardness (GPa) Fracture strength, rf (MPa) Fracture toughness, KIc (MPa m1/2)

Black 1.33 108.9 2.3Yellow 0.48 32.4 1.0


exoskeleton were studied using both micro- and nanoindentation techniques [235,237].The hardness and sti!ness of the exocuticle (outer layer) are higher than those of endoc-uticle (inner layer) as shown in Fig. 113 (b). This is due to the dense twisted plywood struc-ture in exocuticle compared to the coarse twisted plywood structure in endocuticle(Fig. 113a).

7.4. Keratin-based materials: hoof and horn

Keratin consists of dead cells that are produced by biological systems. The most com-mon examples are hairs, nails, hooves, and horns. We briefly describe the later two.

The complex design of equine hoof wall consists of two structural elements: tubules andintertubular material [241–244]. Fig. 119a shows the schematic of the equine hoof wall.Hollow tubules occupy half of the wall and are parallel to the surfaces. The intermediatefilament, a fibrous structure of keratin, is embedded in the keratin matrix and is composedof a-helical protein bundles with a diameter of 8 nm. In the innermost wall, the interme-diate filament is mainly oriented along the tubule axis and placed horizontally in the inter-tubular material, shown in Fig. 119b. In the mid wall region, the intermediate filament inintertubular material is arranged in helical fashion with angles from 0" to 33". This com-plex design of the hoof wall provides a wide range of mechanical properties in 0–100% ofhumidity condition. As the water content increases, the Young’s modulus decreases. Thise!ect can be dramatic. Fig. 120 shows the initial Young’s modulus plotted as a function ofwater content. The mechanical role of the tubules and orientation of the intermediate fil-aments are to control the crack propagation process and enhance fracture toughness of thewall. Fig. 121 shows that the J-integral of the hoof wall is not very sensitive to the rate ofload application. The average J-integral is 12 ± 3 kJ/m2; the hoof wall prevents brittle

Fig. 117. (a) Stone crab, Menippe mercenaria, chelae showing dark and light-colored region. (b) SEMphotograph showing high level of porosity in yellow exoskeleton material. (c) SEM photograph showing highlevel of porosity in black exoskeleton material (from Melnick et al. [240, p. 2901, Figs. 4–5]).


failure in the entire strain rate range investigated: 1.6 · 10&3 ! 70 s&1. This covers mostsituations encountered by ungulates.

The structure of the rhinoceros horn is similar to the hoof; it has a laminated structureof tubules shown in Fig. 122 [245]. Horn tubules are more closely placed to each otherthan hoof tubules. The mechanical properties of the oryx horn have been studied and com-posite theory has been applied to predict the sti!ness [246]. Viscoelastic behavior of thegemsbok horn has been investigated at di!erent water contents [247]. Fig. 123 showsstress–strain curves of horn along transverse and longitudinal directions [248]. There isa great degree of anisotropy with the strength in the longitudinal direction (parallel tothe tubules) being approximately 10 times that in the transverse direction (perpendicularto tubules).

8. Biological elastomers

8.1. Skin

The skin has multifunctionalities such as temperature regulation, barrier betweenorganism and environment, and even camouflage from predators. Basically, the layered

Fig. 118. Scanning electron micrographs (SEM) taken from fractured specimens of lobster Homarus americanusshowing the hierarchical structure. The honeycomb-type arrangement of the chitin–protein fibers is visible athigher magnifications (from Raabe et al. [234, p. 6, Fig. 5]).


Fig. 119. (a) Schematic of hoof wall; (b) the orientation of intermediate filament in inner wall and mid-wall (fromKaspi and Gosline [244, p. 373, Fig. 1 and p. 374, Fig. 2]).


structure of the skin is composed of the epidermis and dermis layers. The epidermis is aprotective layer of the skin and consists of several layers shown in Fig. 124 [79]. The out-ermost layer of the mammalian skin is stratum corneum made from thin soft keratin. Stra-tum corneum plays a role as a barrier between environment and organism [249,250].Dermis is a connective tissue between epidermis and organism. Primary proteins of thedermis are elastin and collagen. Elastin has an outstanding elastic property andFig. 125 shows the stress–strain curve. Collagen is the main source of the mechanical

Fig. 120. Initial Young’s modulus as a function of water content (from Betram and Gosline [241, p. 130] andKaspi and Gosline [243, p. 1646, Fig. 8]).

Fig. 121. J-integral of hoof wall at di!erent strain rate (from Kaspi and Gosline [243, p. 1132, Fig. 9]).


properties of skins and elastin is not significant. Elastin is responsible for the small defor-mation of the skin and helps it to recover to the original position [251].

Wu et al. studied mechanical properties of stratum corneum as a function of tempera-ture and under di!erent environmental conditions (humidity) as shown in Figs. 126aand b [252]. The strength is decreased with an increase of humidity and temperature. Theyalso studied the role of lipids in the stratum corneum and found that delipidized samplesprovide higher mechanical strength as shown in Fig. 126c and d. The maximum delamina-tion energy of untreated stratum corneum is 8 J/m2 and that of delipidized stratum corneumis 13 J/m2 at low temperature. The mechanical properties of skin vary with age [253].Fig. 127 shows the ratio of the recovered deformation, UR, and initial deformation of skin,

Fig. 122. Transverse section of rhinoceros horn showing six tubules (magnification 220·) (from Ryder [245, p.1195, Fig. 1]).

Fig. 123. Stress–strain curves of horn (adapted from Druhala and Feughelman [248, p. 381 Fig. 8]).


UE as a function of age; this represents elastic recovery of skin after deformation. The elas-ticity of skin continuously decreases with age [253]. The skin strength is also strain-ratesensitive [254]. Fig. 128 shows Young’s modulus plotted as a function of strain rate. Asthe strain rate increases, the elastic modulus also increases. This is typical of viscoelasticmaterials.

Fig. 124. Structure of mammalian skin (from Fraser and Macre [79, p. 208, Fig. 1]).

Fig. 125. Stress–strain curves of elastin (reproduced from Fung [24, p. 240, Fig. 7.2:1]).


Fig. 126. Mechanical properties of stratum corneum; (a,b) peak stress and delamination energy of stratumcorneum with variation of temperature and humidity ;(c,d) peak stress and delamination energy of delipidized anduntreated stratum corneum with variation of temperature and humidity (fromWu et al. [252, p. 783, Fig. 3 and p.784, Fig. 4]).

Fig. 127. Skin elasticity recovery /extensibility ratio (UR/UE) as a function of age for high torque and low torque(from Esco"er et al. [253, p. 351, Fig. 7]).


Both structure and mechanical property di!erences exist over the body and in all mam-malian animals [249]. For example, the rhinoceros has an amazingly thick and tough skinfor protection. Figs. 129a and b show collagenous rhinoceros skin of flank and belly; thethickness is 25 mm and 15 mm, respectively [255]. The tensile strength of the dorsolateral(flank) skin is 30.5 MPa and, compressive strength is 170 MPa. This is much higher thanother mammalian skin. The average toughness of dorsolateral skin of rhinoceros is 77 kJ/m2, which is higher than the maximum toughness of rat skin, 30 kJ/m2 [256]. Fig. 130shows stress–strain curves of three collagenous materials; the schematic in the Fig. 130shows the orientation of the collagen fibers. The highly aligned collagen fibers in the ten-don provide the highest strength and sti!ness (!80 MPa). Cat skin, on the other hand,exhibits a large elastic strain of (!1), due to the loose arrangement of fibers. Rhinocerosskin has the same strength as cat skin, but much less elasticity because the collagen mol-ecules are extended.

8.2. Muscle

The maximum force that a muscle fiber can generate depends on the velocity at which itis activated. Fig. 131 shows the stress that can be generated as a function of strain rate for‘‘slow-twitch’’ and ‘‘fast-twitch’’ muscles. We use slow-twitch muscles for long-rangeevents (e.g., distance running) and fast-twitch muscles for explosive activities, such assprinting or throwing a punch. Both muscles show a decreasing ability to generate stressas the strain rate is increased. However, the fast-twitch muscles show a lower decay.

The plot shown in Fig. 131 is only schematic and represents the rat soleus (slow-twitch)and extensor digitorum longus (fast-twitch). The equation that describes the response inFig. 131 is called the Hill equation [257]. It has the form

"r% a#"_e% b# $ "r0 % a#b "43#

Fig. 128. Young’s modulus of rat skin plotted as a function of strain rate (adapted from Vogel [254, p. 82,Fig. 3]).


where r0 is the stress at zero velocity (equal to 200 kPa in Fig. 131). The range of r0 isusually between 100 and 300 kPa. a and b are parameters and _e is the strain rate (obtainedfrom the velocity).

8.3. Blood vessels

The vascular system provides the transport of nutrients, oxygen, and other chemicalsignals to the various parts of the body. It is divided into two subsystems: pulmonaryand circulatory system. We will not go into any details of the pathology of these two sub-systems. Rather, we will concentrate on their mechanical properties. Arteries (which carryblood from the heart to the various parts of the body) and veins (that collect blood back tothe heart) exhibit some significant di!erences in structure. Arteries are exposed to higherpressures and fluctuations associated with the diastolic and systolic portions of the cardiaccycle. Fig. 132 shows the longitudinal and normal sections of an artery. The structure is

Fig. 129. Skin of the rhinoceros; (a) the skin of flank; (b) the skin of belly (from Shadwick et al. [255, p. 417,Fig. 4]).


layered with three distinct regions: tunica intima (innermost), tunica media (middle), andtunica adventitia (outermost).

Bursting (longitudinal splitting) of blood vessels or aneurysm (tensile instability form-ing a local bulge) are highly undesirable but all too frequent events in humans. There aretwo unique aspects of the mechanical response of arteries and veins that are instrumental

Fig. 130. Stress strain curves of collagenous materials (from Shadwick et al. [255, p. 417, Fig. 11]).

Fig. 131. Stress vs. strain rate for slow-twitch and fast-twitch muscles.


in minimizing the chance of the aforementioned problems: non-linear elasticity and resid-ual stresses.

Fig. 132. Cross-section of an artery and vein, composed of the endothelium, tunica intima, tunica media, andtunics adventitia.

Table 17Dimensions and composition of blood vessels

Vessel Dimensions (mm) Composition

Artery Aorta Diameter 25Thickness 2

Medium-sized artery Diameter

4Thickness

1

Vein Diameter 20Thickness 1


8.3.1. Non-linear elasticityThe three layers comprising blood vessels have di!erent functions and compositions.

Table 17 summarizes the similarities and di!erences between arteries and veins, includingmain vessels such as the aorta. The composition of arteries is made up primarily of elasticfibers (elastin), collagen, and smooth muscle. Compared to veins, arteries contain muchmore elastic material. Thicker arteries, such as the aorta, contain less smooth muscle thanboth smaller arteries and also veins. These di!erences account for the ability of arteries toresist large pressure fluctuations during the cardiac cycle.

The mechanical response of blood vessels is shown in Fig. 133a. This is the longitudinalstress–strain response of human vena cava. The response is non-linear elastic. We knowthat it is elastic because on unloading the artery returns to its original dimension. How-ever, there is a slight hysteresis on loading and unloading, due to viscoelastic processes.The slope approaches infinity as the strain approaches 0.3. This increase in slope is dueto the extension of the collagen and elastin fibers. If they are stretched beyond this point,failure takes place. Instead of the strain, e, the stretch ratio (k = e + 1) is used in the plot.

It is instructive to plot the slope, dr/de = E, as a function of stress. This is done inFig. 133b for the aorta of a dog (circumferential strip). The slope first increases by a rela-tionship that can be described by a power function. Then, it reaches a linear range, inwhich the increase is more gradual. This non-linear elastic behavior is a characteristic fea-ture of many soft tissues in the human body. It serves as an important function: as thepressure in the blood vessels is increased, the vessels become sti!er.

This response, typical of arteries, has been successfully represented by the equation:

r $ "r+ % b#ea"e&e+# & b "44#

where a and b are parameters defined in Fig. 133b. a is the slope of the linear portion and bis related to the intercept. r* and e* correspond to the onset of the linear portion. Thisequation is known as the Fung equation. This equation can also be expressed in termsof k, the stretch ratios.

8.3.2. Residual stressesBiological materials such as arteries contain residual stress. In the case of a segment of

artery that is not under internal blood pressure, the walls of the artery are under strain andtherefore, have residual stress. Fung [25] has shown that if one makes an axial cut in thewall of an artery, the artery will spontaneously open. This geometry is known as the zero-stress state. The angle by which the artery springs open is defined as the opening angle. Asthis opening angle increases the stress distribution in the wall under pressure becomesmore uniform. This makes sense since under normal blood pressure arteries inflate, caus-ing higher strain on the inner wall of the artery (compared to the outer wall). In arteries,stress is an exponential function of strain, so the observed increase in strain at the innerwall will be accompanied by an increase in stress at the inner wall.

Four di!erent arteries, with di!erent zero-stress angles, are shown in Fig. 134: a = 0",10", 70", and 155". For the same arteries, the wall under pressure stresses at two values ofthe applied internal pressure are shown. For zero pressure, there is a detrimental e!ect onthe stress distribution. However, this is not the critical condition. For 100 mm internalpressure (in the range of pressure of blood inside our body), the artery with the highestvalue of a has the lowest stress in the wall. Thus, the residual stress reduces the maximumstress in the artery walls.


Fig. 133. (a) Stress–strain response of human vena cava: circles-loading; squares-unloading; (b) representation ofmechanical response in terms of tangent modulus (slope of stress–strain curve) vs. stress (adapted from Fung [24,p. 325]).


8.4. Mussel byssus

The byssal threads of marine mussels act as the only anchor lines which attach the ani-mals to reefs, rocks, and other fixtures. These thin hair-like fibers undergo repeated shockfrom pounding waves and changing currents and must survive without failure to preventthe animal from being swept out to sea. Thus, the toughness the byssal thread material

Fig. 134. Residual stresses in arteries; the artery is sliced longitudinally and the angle a is measured (from Fung[25, p. 384, Fig. 11.3.2]).

Fig. 135. Schematic representation of mussel byssal threads (from Qin et al. [260]).


is of the utmost importance. On the macro scale the threads are composed of both a sti!tether region (the distal thread) which is attaches to rock, and an elastic region (the prox-imal thread) which acts as a shock absorber for the animal [258]. The microstructure of bys-sal threads is roughly similar to that of tendons. The distal region consists of many bundlesof collagen fibrils separated by fibrion-like domains and histidine-rich blocks, includingpossible b-sheet regions [259–261]. An illustration of the byssal thread micro and macro-structure is presented in Fig. 135 [261]. Although these threads are similar to tendons in ten-sile strength, the distal region is remarkably more extensible and much tougher [258].

The two regions of the thread serve di!erent functions and thus have very di!erentmechanical properties. The elastic modulus of the proximal thread is approximately anorder of magnitude lower than that of the distal region [258]. However, failure almostexclusively occurs in the proximal region [262]. This implies the distal region is consider-ably tougher, as can be seen from the area under the curves in Fig. 136 [262].

The mismatch in elastic modulus of the two regions presents an interesting MaterialsScience problem. Failure often occurs at the interface of joined materials with high mod-ulus mismatches [263,264]. This does not occur in the case of the byssal threads and islikely the result of modulus management in which the distal region softens and the prox-imal portion sti!ens close to the interface.

8.5. Cells

Cells constitute the basic structural building blocks of living organisms and perform avariety of functions: self-replication, protection from the environment, acquisition ofnutrients, movement, communication, catabolism of extrinsic molecules, degradationand renewal of aged intrinsic molecules, and energy generation.

8.5.1. Structure and mechanical propertiesMost of the biological cells are 1–100 lm in size, and they comprise many constituents

(Fig. 137a) [265]. The interior of the cell includes a liquid phase (cytosol), a nucleus, the

Fig. 136. Stress strain curve of the Distal and Proximal region of the mussel byssal thread (reproduced from Belland Gasoline [262]).


cytoskeleton consisting of networks of microtubules, actin and intermediate filaments,organelles of di!erent sizes and shapes, and other proteins. The exterior of the cell is cov-ered by a phospholipid bilayer membrane reinforced with protein molecules (Fig. 137b).

Fig. 137. Eukariotic cell structure and elastic properties (from Bao and Suresh [265, Fig. 1]).


The resistance of single cells to elastic deformation, as quantified by an e!ective elasticmodulus, ranges from 102 to 105 Pa (Fig. 137c), orders of magnitude smaller than thatof metals, ceramics and polymers. The deformability of cells is determined largely bythe cytoskeleton, whose rigidity is influenced by the mechanical and chemical environ-ments including cell–cell and cell–extracellular matrix (ECM) interactions.

Living cells are constantly subjected to mechanical stimulations throughout life. Thesestresses and strains can arise from both the external environmental and internal physiolog-ical conditions. Depending on the magnitude, direction and distribution of these mechan-ical stimuli, cells can respond in a variety of ways. For example, within the body, fluidshear of endothelial cells activates hormone release and intracellular calcium signalingas well as sti!ening the cells by inducing rearrangement of the cytoskeleton. The mechan-ical compression of cells, such as chondrocytes, is known to modulate proteoglycan syn-thesis. Furthermore, the tensile stretching of cell substrate can alter both cell motility andorientation. As a result, to understand how cells mechanically respond to physical loads isan important first step to further investigate how the transmission and distribution of thesemechanical signals are eventually converted to biological and chemical responses.

8.5.2. Mechanical testingWith the recent advances in molecular and cell biology, biophysics, nanotechnology,

and materials science, several innovative experimental techniques and equipments havebeen developed to probe the structural mechanical properties of biostructures from themicro down to the nanoscale. These techniques can not only perform direct mechanicalprobing and manipulation of single cells and biomolecules, but also allow such tests tobe conducted under physiological conditions. Lim et al. [266] summarized biomechanicaltesting and imaging instruments/techniques employed to study biological structures rang-ing from single biomolecules, cells to tissues, as shown in Fig. 138. Fig. 138a shows someof the experimental techniques used for conducting biomechanical tests in single cells andsingle molecules while Fig. 138b shows the imaging techniques available for use in suchtests. Bao and Suresh [265] further classified the experimental techniques into three types(Fig. 139):

Type A: local probes in which a portion of the cell is deformed.Type B: mechanical loading of an entire cell.Type C: simultaneous mechanical stressing of a population of cells.

Atomic force microscopy (AFM) and magnetic twisting cytometry (MTC) belong totype A. AFM has become a powerful technique for both imaging surface morphologyand sensing force. A sharp tip mounted at the end of a flexible cantilever directly contactsthe sample surface and generates a local deformation (Fig. 139a). The interaction betweenthe tip and sample surface induces deflection of the cantilever, which can be calibrated toestimate the applied force. Fig. 140 represents the deformation and unfolding of protein byAFM. Magnetic twisting cytometry (MTC) involves magnetic beads with functionalizedsurfaces. Magnetic beads are attached to a cell and a magnetic field imposes a twistingmoment on the beads, deforming a portion of the cell (Fig. 139b). Deformation generatedby magnetic beads is analyzed and the mechanical properties of the cell can be obtained.

Micropipette aspiration (MA) and optical tweezers are common methods of type B. Asuction pressure was applied through a micropipette to deform a single cell (Fig. 139c).


The shape change of the cell is recorded by video microscopy. By measuring the elongationinto the pipette as a result of the suction pressure, the mechanical properties can be eval-uated. Micropipette aspiration is widely used to study the mechanical response of blood

Fig. 138. (a) Experimental techniques for conducting mechanical tests in single cell and single moleculebiomechanics. (b) Imaging techniques that can be used to observe physical, biological and biochemical changesoccurring in biological structures during biomechanical tests of cells and biomolecules (from Lim et al. [266]).


cells. Optical tweezers or laser traps use laser to control particles in a medium. When alaser beam shines on a dielectric particle with higher refractive index than the medium,the gradient force is higher than the scattering force. As a result, a net force pushes theparticle towards the focal point of the laser. In order to deform a single cell, a laser trapis used with two microbeads attached to the opposite ends of a cell (Fig. 139d).

Shear-flow methods (Fig. 139e) and stretching devices (Fig. 139(f)) are type C methodsused to study the mechanical response of an entire population of 102–104 cells. Shear-flowexperiments are conducted with either a cone-and-plate viscometer or a parallel-plate flowchamber. The shear stress applied to cells for both cases can be quantified. Di!erentstretching devices (uniaxial, biaxial, and pressure-controlled) have been developed todeform cells. Cells are cultured on a thin polymer substrate, which is coated with extracel-lular matrix (ECM) molecules for cell adhesion. The substrate is then mechanicallydeformed while maintaining the cell’s viability in vitro. The e!ects of mechanical loadingon cell morphology, phenotype and injury can be examined.

The developments and advances in nanotechnology and biophysical techniques enablea better understanding of the pathophysiology and pathogenesis of human diseases thatmanifest structural and mechanical properties changes. Recent works by Lim [267] andLee and Lim [268] highlighted some of the biomechanics research carried out on severaltypes of diseases, such as malaria, sickle cell anemia, and cancer.

Fig. 139. Schematic representation of di!erent types of experimental techniques used to probe living cells (fromBao and Suresh [265, Fig. 2]).


The human red blood cell, which has a biconcave shape with an average diameter ofabout 8 lm is highly deformable. During the circulation in the narrow capillaries (about3 lm in diameter), it undergoes severe deformation and transforms the biconcave shape tobullet shape by folding. The cell fully recovers its original shape after it flows throughsmall capillaries. Blood cells can harden and lose their elasticity through disease, suchas malaria and sickle cell anemia. The change in mechanical properties causes seriousimpairment of blood flow and results in severe anemia, coma, or even death. Sureshand coworkers [269–272] studied the mechanical response of living cells. Ingenious exper-imental techniques developed in collaboration with Lim enabled establishing the loadextension response of a single cell. From this, the researchers extracted the elastic responseof the cell and how it is altered by disease. Figs. 141a and b show the conceptual experi-ment [271]. Two glass beads (diameter of approximately 5 lm) attach themselves to theends of the cell by capillary forces. A laser beam is used to trap one of the beads. Thisis an optical (laser tweezer) trapping device. The glass slide under the cell is moved andthe load is measured. The displacement of the cell is recorded. The actual photographsof the cells as they are being stretched are shown in Fig. 140c and d. This information thusobtained is compared with computational simulations using both a finite element meshand a new approach based on actual spectrin fibrous molecules, developed by the MIT

Fig. 140. Domain deformation and unfolding of a multidomain protein under stretching with AFM (from Fisheret al. [274]).


group (Fig. 140e). Fig. 142 shows the molecular based and continuum models of red bloodcell membrane [271]. Lim et al. [273] have a comprehensive review on mechanical modelsfor living cell.

8.5.3. Cell motility, locomotion, and adhesionMost cells have the ability to move. Some cells are specialized for locomotion, such as

amoebae and spermatozoids. In most cells, locomotion is usually repressed. However, thisability can be activated in wounds and oncogenesis. The mechanism of amoeboid cellmotility (crawling, or gliding) involves the actin cytoskeleton. Actin filaments themselvesare likely to be involved in the force-generating mechanisms. The major components ofcell motility are shown in Fig. 143 [275]. Protrusion is the forward motility of the mem-brane at the front of the cell. Adhesion of the advancing portion of cell is required for pro-trusion to be converted into movement along the substrate. The last step in locomotion iscomprised of two mechanistically distinct processes: de-adhesion and tail retraction.

The protrusion at the front of motile cells requires dense arrays of actin filaments. Itseems that these filaments are organized with their barbed ends oriented preferentiallyin the direction of protrusion. The web of actin filaments is organized as an orthogonalcross-weave between two sets of filaments oriented at approximately 45" to the directionof protrusion Two mechanisms for generating protrusive force have been proposed:

(a) The action of motor proteins to drive protrusion: Myosin I molecules contribute tothis, just as in the case of muscles (Section 8.2); myosin I moves toward the actin fil-ament barbed ends.

Fig. 141. (a,b) Schematic representation of single cell extension apparatus; (c,d) photomicrographs of red bloodcells in extended configuration; (e) spectrin fiber simulation of process; initial unstretched configuration shown(from Dao et al. [271]).


(b) Actin polymerization itself produces force. Polymerization of pure actin inside alipid vesicle can deform the cell membrane; polymerization of other proteins alsoproduces membrane-deforming force.

Fig. 142. Molecular based and continuum models of red blood cell membrane. (a) Schematic drawing of the redblood cell membrane structure (not to scale). (b) Molecular based model. (c) E!ective continuum membrane. (d)Large-strain response of ‘‘single-crystal’’ worm-like chain membrane (p = 8.5 nm, L0 = 87 nm, Lmax = 238 nm)for two area-preserving shear paths J1 and J2 (from Dao et al. [271]).


Force production requires an energy source and this derives from the chemical energyof nucleotide hydrolysis in the ATPase motor. In the polymer model, thermally drivenmovements create the movement.

Cell motility is an important property, especially since it is involved in diseases such ascancer metastasis. The cancer cells separate themselves from the primary tumour, passthrough the extracellular matrix in the body and enter the circulatory system. Then, afterbeing arrested, they penetrate through the blood vessel walls (extravasation) at a second-ary location. This sequence is shown in Fig. 144. Indeed, the application of Mechanics andMaterials Science to the study of cancer cells will hopefully help in elucidating the basicmechanism. Suresh [276] reviews the subject and presents a framework for this new fieldof investigation, which will incorporate cancer cell mechanics, motility, deformability, dif-ferentiation, and neoplastic transformation.

In the adhesion of cells to the extracellular matrix (ECM) or to other cells the proteinintegrin plays a key role. Integrin-mediated adhesion is a complex process. Integrins playan important role by providing anchorage that ensures cell survival, and migration (motil-ity). Integrins are important in how cells react to implants, in tissue engineering, and inhow cells behave in cell arrays and biotechnology cell culture. Fig. 145 [277] shows sche-matics of cells attaching themselves to synthetic biomaterials whose surfaces were modifiedby di!erent means:

(a) proteins adsorbed from solution, such as blood, plasma, or serum;(b) ligands engineered at the surface, such as RGDs (arginine–glycine–aspartic acid);(c) ligands deposited by cells, e.g., collagen deposition.

Fig. 143. Sequence motility showing elements involved in the locomotion of cell; protrusion–adhesion–traction–de-adhesion and tail retraction (reproduced from Mitchison and Cramer [275, Fig. 1]).


Fig. 144. Schematic diagram showing di!erent stages of cancer metastasis; cancer cells penetrate through ECMand into the blood stream, then extravasate into secondary site, where metastasis takes place (from Lee and Lim[268, Fig. 5]).

Fig. 145. Mechanisms controlling cell adhesion to biomaterials (from Garcia [277, Fig. 1]).


Fig. 146. Examples of cellular materials (a – cork; b – balsa; c – sponge; d – cancellous bone; e – coral; f –cuttlefish bone; g – iris leaf; h – stalk of plant) (from Gibson and Ashby [28, p. 17, Fig. 2.5]).


9. Biological cellular materials

Many naturally occurring materials are not fully dense, i.e. they possess internal cavi-ties. This type of design is intentional, since it reduces the density. Examples are cork,bones, wood, sponge, and plant stalks and they are shown in Fig. 146 [28].

Modern synthetic materials have also adopted this form, and we have metallic, ceramic,and polymeric foams. Some are of common and every day usage, such as Styrofoam. Oth-ers are quite esoteric, such as the Space Shuttle tiles, which have a density of 0.141 g/cm3

and a maximum temperature capability of 1260 "C.An example of a biological cellular material is cancellous bone. Bone is designed to have

a variable density. Regions subjected to higher stress are denser. The outside surface ismade of high density material and is called compact bone. The inside of bone tends to havea lower density and is termed cancellous bone. Figs. 81a and 147 show the longitudinal sec-tion of a tibia. The same occurs in antlers. Fig. 81b shows the cross-section of an elk antler.The surface region is compact, whereas the center is cellular. This is also justified by theresistance to flexure: the inside is not subjected to such high stresses as the outside (rar,where r is radial distance). Thus, the strength requirement increases linearly from the neu-tral axis to the surface. This corresponds approximately to the porosity distribution.

There are numerous other examples of cellular materials. These cellular materials areused either by themselves or in sandwich arrangements. Sandwich structures range fromcommon cardboard used in packaging to important uses in the aircraft industry. The basicidea is to have a dense skin and a light-weight interior. Fig. 148 shows a cross-section of ahorseshoe crab, where we can see that a cellular network provides the rigidity [278]. Twoother examples, wood and beak interior, are described in Sections 9.2 and 9.3, respectively.

9.1. Basic equations

The compressive stress–strain curves of cellular materials have three characteristicregions: (a) an elastic region, (b) a collapse plateau, and (c) a densification region. These

Fig. 147. Longitudinal section of tibia (from Gibson and Ashby [28, p. 430, Fig. 11.1]).


are shown in Fig. 149 [28]. The higher the initial density, expressed in Fig. 149 by q*/qs, thesmaller the collapse plateau region. It also occurs at a higher stress.

We will develop expressions that predict this behavior. These are the Gibson–Ashbyequations. They are developed here for an open cell geometry that represents well cellularmaterials with a low relative density. Section 9.3.2 will present the equivalent equations fora closed cell geometry. Fig. 150 represents this open-cell structure. It consists of straightbeams with a square cross-section [28]. The model is very simple but captures the essentialphysics. There are two characteristic dimensions: the cell size, l, and the beam thickness, t.

Fig. 148. (a) Cross-section image of horseshoe crab exoskeleton showing the foam structure. (b) SEMmicrograph shows the detail of the foam structure in horseshoe crab exoskeleton (from Chen et al. [278]).


(a) Elastic region

Three elastic constants are defined for an isotropic foam: E*, G*, and t*. The density ofthe cellular material is q*, and that of the solid material is q. From Fig. 150 we can obtainan expression for the density in terms of l and t

Fig. 149. Stress–strain curves for cancellous bone at three di!erent relative densities: 0.3, 0.4, and 0.5 (fromGibson and Ashby [28, p. 317, Fig. 11.5]).

Fig. 150. Open-cell structure for cellular materials with low relative density. This is the structure upon which theGibson–Ashby equations are based (from Gibson and Ashby [28, p. 185, Fig. 5.6]).


q+

qs

$ C1tl

( )2

"45#

C1 is a proportionality constant. When the cell is subjected to compressive loading, it willdeflect as shown in Fig. 151 [28]. The vertical columns push on the horizontal beams andcause them to bend. A force F on each column produces a deflection d in the beam. Themoment of inertia of a beam with a rectangular section (sides of b and h) is

I $ bh3

12"46#

For the square cross-section with side t

I $ t4

12"47#

Beam theory states that the deflection, d, is given by

d $ C2Fl3

EsI"48#

C2 is a constant. The stress acting on the cell is related to the force, F, by (each force F isshared by two neighboring cells)

r $ Fl2

"49#

Fig. 151. The open cell configuration under compressive loading. Note the deflection d observed (from Gibsonand Ashby [28, p. 185, Fig. 5.6]).


The strain, e, is related to the deflection by

e $ 2dl

"50#

Thus, the Young’s modulus, E*, is

E+ $ EsI2C2l4

$ Est4

24C2l4

This can be expressed as a function of density (Eq. (45))

E+

Es$ C1

24C2

q+

qs

$ %2

"51#

Experimental measurements indicate that C1/24C2 should be approximately equal to one.Thus

E+

Es! q+

qs

$ %2

"52#

Similarly, an expression for the shear modulus can be obtained

G+

Es$ 3

8

q+

qs

$ %2

"53#

(b) Plastic plateau

At a certain level of deformation, elastic behavior gives way to plastic deformation. TheGibson–Ashby equations are based on the formation of plastic hinges at the regions wherethe beams terminate. Four of these plastic hinges are circled in Fig. 151.

For the elastic case, the stresses increase linearly from the neutral axis. For the case of aplastic hinge, r = rys, the stresses acting on the cross-section are uniform and tensile abovethe neutral axis and uniform and compressive below the neutral axis. Fig. 151 shows theconfiguration.

The plastic moment, Mp, about the neutral axis is

Mp $ Ft2

"54#

The yield stress is related to F by

rys $F

tt2

"55#

Thus, substituting Eq. (54) into Eq. (55)

Mp $1

4ryst3 "56#

But, taking the beam with length l/2 and considering the force F/2 applied to each of thetwo hinges

Mp $F2

l2$ 1

4Fl "57#


The global stress acting on the foam is the force F divided by the area upon which it acts, l2

r+pl $

Fl2

"58#

Equating Eqs. (56) and (57) and applying Eq. (58)

r+pl

rys$ t

l

( )3

"59#

Substituting Eq. (45) into Eq. (59)

r+pl

rys$ C&3=2

1

q+

qs

$ %3=2

"60#

There are other expressions for the closed-walled cell, for cells that do not undergo plas-tic deformation, and for other cases.

(c) Densification

Densification starts when the plastic plateau comes to an end. This region is character-ized by a complex deformation pattern. The stresses required for the densification rise rap-idly as the open spaces between the collapsed cell structure close up. The analyticaltreatment for the collapse of pores and voids will not be presented here. There are theoriesthat address this problem. One of the best known, the Carroll–Holt–Torre theory[279,280], assumes a spherical hole inside a solid sphere. By applying an external pressureit is possible to collapse the internal hole. The smaller the hole is, the higher the stress is.The Helle et al. model [281] addresses the same problem. A third formulation is the Fis-chmeister–Arzt theory [282].

9.2. Wood

Wood is one of the most ancient structural materials in the world and has played animportant role in civilization. It is still widely used in buildings, furniture, ships, musicalinstruments, paper and so on. Wood has high specific sti!ness (sti!ness per unit weight)and specific strength that is comparable with steel [17]. The outstanding mechanical prop-erties are mainly due to the hierarchical structure and optimized reinforcement orientationof cellulose fibrils.

Wood is a cellular composite with four levels of hierarchical structure: molecular, fibril-lar, cellular, and macroscopic structure [283]. Fig. 152 shows the hierarchical structure ofwood [284]. The main structural constituent of wood is cellulose, a high molecular weightpolysaccharide (see Section 5.4, 2) which contributes the sti!ness and strength. The cellu-lose is organized into microfibrils of about 10–20 nm in diameter. The microfibrils consistof both crystalline and amorphous regions. Bundles of cellulose microfibrils further formmacrofibrils which are embedded in an amorphous matrix of lignin, hemicellulose, andother compounds.

The most characteristic structural level is the cellular structure, or the wood tracheid.Mark and Preston [285,286] carried out comprehensive studies on the structure of woodtracheids. Fig. 153a shows a simplified and generalized model of a wood tracheid [287].Cotton fibers, which consist mainly of cellulose, have a similar multilayer structure


Fig. 153. Structure of (a) wood tracheid and (b) cotton fibers showing microfibril orientation and relative size ofdi!erent layers of the cell wall (courtesy of J.O. Warwicker, the Shirley Institute, Manchester, England. [287]).

Fig. 152. Hierarchical structure of cellulose in wood (courtesy of Kaplan [284]).


(Fig. 153b). From the outer surface to the center, the fiber has a cuticle, a primary wall, asecondary wall, a lumen wall, and a lumen. The cuticle is a waxy layer less than 0.25 lmthick. The primary wall is the original cell wall and consists of cellular fibrils in a randomlyoriented network. The primary wall can restrict swelling of fibers. The secondary wall iscomposed of an outer layer (S1), middle layer (S2), and inner layer (S3). The three layersof the secondary wall are built up by lamellae formed by almost parallel microfibrils andstack in a helicoidal pattern. The S1 layer is roughly 0.2–0.3 lm and has an angle of 20–35"with respect to the fiber axis (parallel to the trunk). The S3 layer, also know as lumen wall,is not always detected. It is 0.1 lm thin and has an angle of 60–90". The S2 layer consti-tutes about 95% by weight of the wood tracheid and can be 4 to 5 lm thick. The micro-fibrils in the S2 layer have an angle of 20–30" [288]. The relative cross-sectional area(roughly 80% of the total cell wall area) and the low microfibrillar angle make the S2 layerthe major load bearing component [283]. The macroscopic structure of wood can be seenthrough naked eyes. Growing rings and rays can be observed in most species.

The mechanical properties of wood are highly anisotropic due to the preferred orienta-tion of cellulose fibrils (parallel to the trunk). Gibson and Ashby [28] have a comprehen-sive review on the mechanical properties of wood. Fig. 154 shows three orthogonal planesof symmetry of wood: the radial, the tangential, and the axial directions. The sti!ness andstrength are greatest in the axial direction by a factor of 2–20 than that in the radial andtangential directions, depending on the species.

The general compressive stress–strain curves for wood (balsa wood) in three directionsare shown in Fig. 155a. This curve has the same three stages discussed in Section 9.1 and issimilar to the one for cancellous bone (Fig. 146a). At small strains (less than 0.02), thebehavior is elastic in all three directions. The Young’s modulus in the axial direction ismuch larger than that in the tangential and radial directions. Beyond the elastic regime,the loading curves in the three directions show extensive stress plateaus. The yield stressin the axial direction is much higher than that in the tangential and radial directionsand is followed by a sharply serrated plateau. The plateaus in the tangential and radialdirections are relatively flat and smooth. Compression in the tangential direction causes

Fig. 154. A cross-section through the trunk of a tree showing the radial, tangential, and axial (longitudinal)directions (from Gibson and Ashby [28, p. 390, Fig. 10.1]).


uniform bending and uniform collapse by plastic yielding of the cell walls (Fig. 155b) [289].Compression in the radial direction causes uniform bending and uniform plastic collapse(Fig. 155c). A schematic drawing of the deformation under compressive loading in theradial direction is shown in Fig. 156. This is the mechanism modeled in Section 9.1(Fig. 150). The deformation in the tangential direction is the same.

The mechanism of compressive deformation in the axial direction is quite di!erent(Fig. 155d). In woods of low density, the cell walls collapse by end cap fracture(Fig. 157b). The stress drops until the next layer of end cap is intercepted; then, the stressincreases until the second end cap breaks. The repeated deformation process gives thesharply serrated plateau. In woods of high density, the cell walls collapse by local bucklingof the cell walls (Fig. 157c). As the density of the wood increases, both the Young’s mod-ulus and strength increase.

A most remarkable property of wood is highly anisotropic fracture toughness. Its high-est value is 10 times greater than that of a fibrous composite with the same volume fractionof fibers and matrix. Jeronimidis [290] proposed that the creation of new surface area by

Fig. 155. (a) Compressive stress–strain curves for balsa tree. (b) Tangential compression, with scanning electronmicrographs showing the deformation of the cells. (c) Radial compression and (d) axial compression withscanning electron micrographs showing the deformation of the cells (reproduced from Gibson and Ashby [28, p.397–398, Figs. 10.4(a)–(d)]).


fiber pull-out is responsible for fracture toughness. The cracks due to shearing will openand propagate longitudinally, which allows each cell wall to be pulled apart without beingbroken through. Simulation of the S2 cell walls [291] has shown that when the helical angleof the fibrils is 15–20", there is an optimum compromise between energy absorption and

Fig. 156. Schematic drawing of the deformation of wood cells under loading in the radial direction: (a) no appliedload; (b) cell-wall bending in the linear-elastic range; (c) non-uniform cell collapse by plastic yielding (fromGibson and Ashby [28, p. 401, Fig. 10.9]).

Fig. 157. Schematic drawing of the deformation of wood cells under loading in the axial direction: (a) no appliedload; (b) cell collapse by end cap fracture; (c) cell collapse by local buckling of the cell walls (from Gibson andAshby [28, p. 403, Fig. 10.11]).


reduction in axial sti!ness. Fig. 158 shows the crack propagation in wood along directions(a) parallel and (b) perpendicular to the grain. Whereas it is easy for a crack to propagateparallel, perpendicular propagation to the grain is very di"cult. This fracture mode isanalogous to that of the nacre when the shell is loaded along the direction of its surface;the individual platelets are pulled out and this provides the high toughness. The sap chan-nels can stop cracks from propagating as shown in Fig. 159. When the crack propagatestowards a sap channel, it can either enter it or run around its wall and then stop.

9.3. Beak interior

9.3.1. Toucan and hornbill beaksBird beaks usually fall into two categories: short/thick, and long/thin. The toucan is an

exception. It has a long beak that is also thick, a necessity for food gathering in tall trees.This is accomplished by an ingenious solution, enabling a low density and high sti!ness: acomposite structure consisting of an external solid keratin shell and a cellular core.Fig. 160 shows the toucan and hornbill beaks in a schematic fashion. The toucan beakhas a density of approximately 0.1 g/cm3, which enables the bird to fly while maintaininga center of mass at the line of the wings. Indeed, the beak comprises 1/3 the length of thebird, yet only makes up about 1/20 of its mass. The hornbill beak, consisting of 1/4 of thetotal length, has a density of approximately 0.3 g/cm3. A distinctive feature of the hornbillis its casque formed from cornified keratin layer. The mesostructure and microstructure oftoucan and hornbill beaks reveal a material which is reminiscent of sandwich structures offunctionally graded materials, with components made of foam covered by a hard surfacelayer. Therefore, this biological material serves as a useful source for research and as aninspiration for structural design in engineering.

Figs. 161a and b show optical and scanning electron micrographs of the toucan andhornbill beaks. The structure is similar to cancellous bone and the foams consist of

Fig. 158. Crack propagation in wood: (a) initial crack parallel to the grains; (b) initial crack perpendicular to thegrains (from Gibson and Ashby [28, p. 424, Fig. 10.23]).


asymmetric rod-like structure. Most of the cells in the toucan and hornbill are sealed o! bythin membranes. Thus, it can be considered a closed-cell system. The cell sizes vary withlocation and the closed-cell network is comprised of struts with a connectivity of normallythree or four.

Energy disperse X-ray analysis (Fig. 162a and b) shows that toucan and hornbill ker-atins contain principally carbon and oxygen, which are the main components of the pro-tein. A relatively low content of sulfur in the chemical component of keratin seems topoint out to a low content of cystine, a sulfur-containing amino acid. The beak keratinalso contains minerals as indicated by the presence of calcium, potassium, sodium, andchlorine. The presence of calcium indicates a degree of mineralization that provides thehardness of the keratin. However, the content of calcium is low and is less than 1% inthe keratin of the beak. Fig. 162c and d are in stark contrast with Fig. 162a and b. Thetrabeculae of the foam contain more minerals than the shell of the beak. Distinctively,the trabeculae contain a great amount of calcium, giving rise to the increased hardness.The EDX results can be compared with chromatographic compositional studies from sev-eral bird beaks by Frenkel et al. [292]. It is confirmed here that the keratins of the Toco

Fig. 159. Crack is arrested by a sap channel: (a) a schematic drawing of a crack breaking into a sap channel, (b) aschematic drawing of a crack splitting the wall of a sap channel (from Gibson and Ashby [28, p. 413, Fig. 10.21]).


toucan and hornbill beaks appear to be similar to other bird species with a low sulfur andmineral content. Pautard [80] reported that 0.28% of the pigeon beak is comprised ofcalcium.

9.3.2. Modeling of interior foam (Gibson–Ashby constitutive equations)The most significant feature of the cellular solid is the relative density, q*/qS (the density

of the cellular material, q*, divided by the density of the solid material, qS). Gibson and

Fig. 160. Schematic of the beaks; (a) toucan beak; (b) hornbill beak.


Ashby [28] provide an analytical treatment for the mechanical behavior of a broad rangeof cellular materials.

The toucan beak foam can be considered as a closed-cell system. Deformation of theclosed cells is more complicated than that of open cells. When open-cell foams are

Fig. 161. Images of internal foam structure with three cross-sections and scanning electron micrographs offoams; (a) toucan foam; (b) hornbill foam.


Fig. 162. Energy disperse X-ray results, (a) toucan keratin; (b) hornbill keratin; (c) toucan trabecula; (d) hornbilltrabecula.


deformed, cell wall bending occurs. Deformation of closed-cell foam involves not onlyrotation of cell walls, but also stretching of the membranes and internal gas pressure.

The simplest closed-cell cubic model was introduced to describe the deformation of thefoam. Fig. 163 shows (a) undeformed and (b) deformed cubic closed cells envisaged byGibson and Ashby [28]. The linear elastic region is limited to small strain. The foams madefrom material possessing a plastic yield stress are subjected to plastic collapse when theload is beyond the linear elastic regime. When plastic collapse occurs, there is a long hor-izontal plateau in the stress–strain curve. Eq. (61) represents the response of a closed-cellfoam schematically shown in Fig. 163:

r+pl

rys$ C5 /

q+

qS

$ %3=2

% "1& /# q+

qS

% p0 & patrys

"61#

where r+pl is the plastic collapse stress of foam, rys is the yield stress of the solid portion, C5

is a parameter, / is the ratio of volume of face to volume of edge, p0 is the initial fluidpressure, and pat is the atmospheric pressure.

For the open-cell geometry, the parameter / in Eq. (61) is equal to 1. Additionally, thepressure is unchanged, i.e., p0 & pat = 0. Thus, Eq. (61) reduces to

r+pl

rys$ C5

q+

qS

$ %3=2

"62#

This is the open-cell equation from Gibson and Ashby [28] (Eq. 60, Section 9.1). Theparameter C5has an experimentally obtained value of 0.3 for plastic collapse and 0.2 forbrittle crushing (where r+

pl=rys in Eqs. (61) and (62) is replaced by the normalized crushingstress r+

cr=rfs).The cell shape of toucan and hornbill foams are highly complex and consist of the com-

bination of triangle, quadrilateral, and even higher number of edges of polygons. Thereare circular cells at the nodes, which are shared by several cells. To avoid the complexity

Fig. 163. (a) Gibson–Ashby model for closed-cell foam; (b) deformation of closed-cell foam.


of characterizing cell geometry of toucan and hornbill foams, we measured the relativedensity. The mean value of the density of the toucan foam and that of solids were mea-sured and found to be: q* = 0.05 and q = 0.56. Thus, the relative density of the toucanfoam is approximately 0.09 and that of the hornbill foam is found to be 0.1. This valueis obtained from the foam density, q* = 0.139, and the density of the solid, q = 1.4. Theyield stresses of the toucan and hornbill trabeculae, rys, are estimated from microindenta-tion values (H ' 3ry), which seem to be more accurate than the nanoindentation valuesdue to the size e!ect. This gives values of rys = 91 MPa for toucan and rys = 128 MPafor hornbill.

Fig. 164a shows the predictions from Eqs. (61) and (62) as well as experimental resultsfor a number of materials [293–298]. These equations bracket the experimental resultsquite well. A more detailed plot of the compressive strength for the toucan foam as a func-tion of relative density is shown in Fig. 164b. Although the relative density of toucan andhornbill foams show a small di!erence, the relative yield strength of the hornbill trabeculaeis more than fourfold higher due to the high degree of mineralization. It should be notedthat the membranes are not expected to contribute significantly to the mechanical response

Fig. 164. (a) Experimental results (hollow circles) and Gibson–Ashby prediction for open-cell and closed cellfoams (continuous lines); (b) detailed plot.


of the foam since many of them contain tears due to desiccation. However, one would notexpect this to be the case for the live animal. Gibson and Ashby [28] give values ofC5 = 0.3 and C5 = 0.2 for plastic buckling and brittle crushing, respectively. The responseof the toucan foam is intermediate between the two.

Fig. 165a shows the fracture pattern in the foam. It is composed of a mixture of plasticdeformation, partial, and total fracture of the trabeculae. The trabeculae have a fibrousstructure similar to wood and can fracture partially when they are subjected to bending(Fig. 165b). In other locations, the trabeculae undergo total fracture. Fig. 165c showsan example. The ‘‘green twig’’ appearance of the trabecula is evident in Fig. 165b. Hence,the cellular material does not crumble when compressed to its maximum strain. Rather, itcollapses in a semi-plastic manner.

9.4. Feather

Feathers are very light and sometimes sti! epidermal structures that distinguish theclass of Aves. The basic structure of bird feather is composed of the main shaft, or ‘rachis’and side branches called barbs or ‘rami’. Fig. 166a shows a schematic of feather matchedwith scanning electron micrographs of feather belonging to Blue-and-Gold Macaw (Araararauna). Closed-cell foam can be observed within both the rachis and barb structures[299]. The tertiary structures extending from the barb are called barbules or ‘radii’. Theyare tied together by ‘hooklets.’ Barbs, barbules, and hooklets extending from the rachiscomprise the vane or vexillum of feather. The rachis consists of a hollow cylinder called

Fig. 165. Fracture morphology of closed-cell foam showing profuse trabecula bending; (a) overall view; (b)‘‘green twig’’ fracture; (c) total fracture of trabecula.


‘cortex’ and supporting foam core called ‘medulla’. The rachis is completely filled withmedullary foam at the distal end and has a hollow at the root section or ‘calamus,’ shownin Fig. 166b [299]. X-ray di!raction studies report that the crystallinity and the di!ractionpattern of feather keratin are very similar to that of other avian keratins such as claw andbeak [79]. However, there are di!erences in composition between feather and other avian

Fig. 166. (a) Schematics of feather structure with scanning electron micrographs of macaw feather. (b) Scanningelectron micrographs of a hollow section of macaw rachis (courtesy of S.G. Bodde [299]).


keratins [300,301]. Brush [300] measured the molecular weight of avian keratins and found10,500 g/mol for feather, which is lower than claw and beak keratins which range from13,000 g/mol to 14,500 g/mol.

The bending behavior of foam-reinforced feather rachis is of great importance. Thefeather must have sti!ness and flexibility in order to withstand some degree of bendingcaused by flight activity. The bending behavior of the rachis (feather shaft) has been stud-ied by Purslow and Vincent [302]. They demonstrated that the bending behavior of therachis depends on the size and geometry of the cortex. The calamus of the feather has acircular or square cross-section, which becomes elliptical toward the distal end. Bonserand Purslow found an average Young’s modulus of 2.5 GPa in tension [303]. Young’smodulus of volant bird feather varies with the orientation of the rachis, while that offlightless bird is almost same at any position along the length of rachis [304]. Corninget al. investigated the uniaxial oscillatory strain pattern of feather during the flight andthe peak compressive strain was found to be just over twice the peak tensile strain [305].

Mechanical properties of feather keratin demonstrate humidity sensitivity. Sti!ness offeather rachis decreases with an increased moisture content, which is similar to behavior ofother keratinous tissue [306]. Fig. 167 shows stress–strain curves of feather rachis and clawkeratin for three di!erent humidity levels. The feather rachis is sti!er than claw keratin dueto molecular orientation di!erences. The compressive behavior of the medullary foam wasstudied and the Young’s modulus was found to increase with relative density [307].Fig. 168 shows Young’s modulus revised from Bonser’s results [307] plotted as a functionof relative density.

The relationship between melanin and mechanical properties of the avian keratin hasalso drawn attention after Bonser and Witter described increased hardness of Starling(Sturnis vulgaris) bill associated with seasonal melanization [308]. Butler and Johnson havestudied melanized and non-melanized barbs of feather [309]. They considered not onlycolor but also the location along the rachis of the feather. Fig. 169 shows the breaking

Fig. 167. (a) Stress–strain curve of feather at three di!erent humidity conditions; (b) stress–strain curves of clawkeratin at three di!erent humidity conditions (from Taylor et al. [306, p. 935, Figs. 1 and 2]).


stress as a function of positional distance of the barb along the length of the rachis. Blackdots represent melanic and white dots represent non-melanic regions. In this case, the indi-vidual barb morphology, especially cross-sectional area (which however may not be abso-lutely independent of melanin-induced e!ects). Variation in barb strength was observedalong the rachis from the proximal end, enduring higher stresses during flight, to the distalend. Therefore, mechanical e!ects of melanin were found to insignificant relative to geo-metric variation in feather barb and position along the rachis.

10. Functional biological materials

10.1. Gecko feet and other biological attachment devices

The gecko feet present a fascinating problem of adhesion [310]. This attachment systemhas first recognized by Ruibal and Ernst [311]. Indeed, there are several biological systems

Fig. 168. Relative Young’s modulus vs. relative density of medulla (reproduced from Bonser [307, p. 936, Fig. 2]).

Fig. 169. Breaking stress as a function of fractional distance (reproduced from Butler and Johnson [309, p. 284,Fig. 4]).


in which the attachment to surfaces uses similar principles: flies, beetles, and spiders. Pre-liminary results show that the tree frog might be included in this category [315]. Again,novel experimental techniques coupled with analysis are revealing these mechanisms.The fly and gecko feet are made of a myriad of thin rods, called setae, terminated by spat-ulae, with submicron diameters. These are shown for the fly Calliphora vicina in Fig. 170.Fig. 171a shows a cross-section of the gecko foot with setae marked (st). Each seta has, atits tip, a number of spatulae, marked (sp) in Fig. 171b. Arzt et al. [5,312] and Spolenaket al. [313] calculated the stress required to pull o! a contact. This calculation is basedon the van der Waals forces combined with Hertzian contact stresses. For simplicity,spherical spatulas are assumed, as shown in Fig. 172.

The Hertzian stress is given by

d3 $ 12RFE+ "63#

where R is the radius of the spatula, d is the contact area, F is the adhesion force, and E* isa biaxial elastic modulus. The attractive interfacial adhesion energy per unit area, c, wasadded to the calculation (Johnson, Kendall, and Roberts) leading to the pull-o! force F

F $ 3

2pRc "64#

where c is the adhesion energy per area. The stress required to pull o! a spatula is the forceF divided by the apparent area (see Fig. 172) Aapp

rapp $3

2

f cR

"65#

where f is the fraction of the area covered by setae

f $ pR2

Aapp"66#

Fig. 170. Setae and distal spatulae fly Callifora vicina. Van der Waals forces at spatula-surface interface generateattachment forces that in the gecko can be as high as 20 N (from E. Arzt, MPI, Stuttgart, Germany [5]).


It can be seen that the pull-o! stress is inversely proportional to R. Thus, the larger themass of the biological system, the smaller R has to be. This is confirmed by the experimen-tal plot of Fig. 173. The number density of attachments, proportional to R&2, increaseswith the mass. For geckos, that have a mass of approximately 100 g, it is equal to 1000setae per 100 lm2, or 10 setae per lm2. This is in full agreement with Fig. 170, which showsspatulae having an approximate diameter of 0.2 lm.

Spolinek et al. [313] developed a design map that incorporates both the tensile strengthof setae and the ideal contact strength. This plot is shown in Fig. 174. It represents thefiber radius in the ordinate plotted against the Young’s modulus in the abscissa. Twomajor lines define an inverted cone in which the system should be. The line with negativeslope represents the failure of setae by tension and is obtained from the application of thetheoretical strength (rth = E/10) to Eq. (65). This results in

Fig. 171. SEM micrographs showing the detail of (a) setae; and (b) spatulae (courtesy from E. Artz and G.Huber).


R P3c2rth

$ 15cE

"67#

The second line, on the right side, represents the ideal contact strength and is given by

R P kE2 "68#

k is a parameter incorporating several dimensions. Indeed, the biological systems fall with-in the V region of the plot, showing that the calculations bracket the requirements well.

Fig. 172. Idealized arrangement of attachment system with spherical tip shape (radius R and spacing 2K) (fromSpolenak et al. [313, Fig. 2]).

Fig. 173. Idealized arrangement of attachment system with spherical tip shape (radius R and spacing 2K) (fromArtz et al. [312]).


The biomimicking of this attachment principle is being implemented in synthetic sys-tems. Whereas the paws of a gecko can generate adhesion forces of tens of N, much greaterforces will be hopefully achieved in synthetic systems, and Spiderman is in the realm ofreality.

However, van der Waals forces are not complete story, and capillarity plays a role. Theadhesion force of exerted by a single gecko spatula was measured by Huber et al. [314]

Fig. 175. Force of single seta pulled parallel to surface (preload of 15 lN) (from Autumn et al. [310]).

Fig. 174. Partial adhesion map for a spherical tip shape; thin lines are contours of equal apparent contactstrength; oval section represents the regime of bioattachments (from Spolenak et al. [313, Fig. 10]).


after modifying the substrates. The seta of a gecko was glued to an AFM cantilever.Although work by Autumn et al. [310] indicated that the pull-o! force did not increasewith humidity, this is clearly evident in Fig. 175. The results are expressed analytically as

F $ F drag 1% 1:22Hg

*******AW

AS

r$ %"69#

where H is the humidity, g is a geometrical parameter (!1.2), AW (3.7 · 10&20 J) and AS

(6.5 · 10&20 J) are the Hamaker constants for water and the substrate, respectively.

10.2. Structural colors

Structural color is a phenomenon of wave properties of light. Biological systems areable to produce structural color using highly precise and sophisticated nanometer-scalearchitectures [316]. The coloration of birds has attracted many scientists and is relatedto sexual signaling as is obvious in the case of nuptial plumage change, camouflage,and aggression. The mechanisms of coloration to be discussed are chemical or pigmentaryand physical or structural. And among structural colors, scattering by photonic crystalarrays and interference in thin films will be addressed.

Pigment is greatly responsible for coloration of birds [317]. Melanin and its types are pig-ments responsible for black, grey or brown color. Melanin is secreted by melanocytesembedded in the epidermis. Melanin also serves to increase hardness of bill keratin, as Bon-ser and Witter presented in the case of the seasonal change of bill color in the EuropeanStarling (Sturnis vulgaris) [308]. Bonser and Witter, among other scenarios, proposed that

Fig. 176. (a) SEM of burbles of peacock; (b) SEM of melanin rods embedded in keratin layer (from Zi et al. [318,Fig. 1]).


the harder melanic bill keratin may resist increased abrasion and wear experienced duringforaging in winter months. Carotenoids are di!use organic pigments of which there are twoclasses: xanthophylls, or oxygen-containing carotenoids, responsible for yellow colorationand carotenes, or oxygen-free, producing red coloration. In avian coloration, however,there is no blue pigment. Blue and generally green coloration is possible by structural coloror the interaction between carotenoid pigments and structurally produced color.

10.2.1. Photonic crystal arraysPhotonic structures are widely distributed in nature, such as in feathers, scales, or insect

cuticles. In birds, blue color is produced when light is scattered coherently from an arrayof melanin granules suspended in a matrix of keratin and air vacuoles in the feather parts,for example. Iridescence such as that observable in the peacock’s (Pavo muticus) feather isproduced by interference. Fig. 176a shows scanning electron micrographs of peacock bar-bules [318]. The barbules are composed of medullary core bound by a melanin-containingcortex and encased by a thin keratinous cuticle. In this case, a periodic array of melaninrods is observable in the cortex, shown in Fig. 176b. By varying the lattice constants insimulation of the 2-D photonic-crystal-like structure, Zi et al. were able to vary the wave-length of the scattered light.

Structural coloration is not limited to the class of Aves; it is observed in fish and ininsects such as butterflies (lepidoptera), discussed in Section 10.2, or beetles (celeoptera).One of the most striking examples of color-producing structures is that present in the Lep-idoptera (butterflies and moths) species, including the tropical Morpho family [319–322].The Morpho butterflies are among the largest in the world with a wingspread of 7.5–20 cm. The males of Morpho menelaus have brilliant blue coloration on the dorsal sidewings and camouflaged brown color on the ventral side of the wings. Such designs helpthem to elude potential predators, birds, for example. When they fly, the top surfaces ofwings continuously change from metallic blue to dull brown as the angle of the light strik-ing the wing changes. They seem to disappear and then reappear a distance away duringflight. Coupled with the unpredictable pattern of flight, the ability to change color makesthem di"cult for predators to pursue. When the Morpho butterflies land, they close theirwings completely, showing the camouflaged brown underside of wings that matches thesurrounding and protects them from being found.

The blue color of Morpho butterfly comes from the well-defined structure of the wings.This is another example of hierarchical structure from nanometer, micrometer, to millime-ter found in nature (Fig. 177 [316]). The wings of butterflies and moths consist of a trans-lucent membrane covered by a layer of scales. Butterfly scales are comprised of chitin,

Fig. 177. Hierarchical structure of the butterfly, Morpho rhetenor wing: (a) wing; (b) scales; (c) ridges (top view);(d) ridges (cross-section). Scale bars (a) 1 cm; (b) 50 lm; (c) 1.8 lm; (d) 1.8 lm (from Vukusic and Sambles [316]).


which is a white colored polysaccharide widely found in arthropod cuticles [321] (see Sec-tion 5.4). Each scale is a flattened outgrowth of a single cell that fits into a socket on thewing and is about 100 lm long and 50 lm wide. The scales overlap like roof tiles and com-pletely cover the membrane, appearing as dust to the naked eye. Each scale is covered bylongitudinal ridges joined at intervals by cross-ribs, as shown in Fig. 178a [319]. Ridgesand cross-ribs frame a series of windows that open into the interior of the scale, wherethe pigment granules are located. For more radiant color observed in other species, theridges are much higher and have very precise nano-structure. The cross-sectional viewof ridges reveals the discretely configured multiple slits, which are spaced 200 nm apart.Interference occurs when light waves striking the wing interact with light waves reflectedby the wing. Though sunlight contains a full range of light wavelengths, only high-energywaves survive scattering events. The periodicity of the nano-structure defines a reflectedwavelength of blue light, ranging from 400 nm to 480 nm [319,320]. Fig. 178b [319] showsthe detailed grating responsible for interference. There is frequently a background layer ofa dark pigment such as melanin which absorbs low-energy waves, perhaps serving to inten-sify the reflected blue color.

10.2.2. Thin film interferenceAs another example of structural coloration, the feather of Hadeda Ibis, Bostrychia

hagedash, has been studied [323]. At first glance, the plumage of this species appears dullbrown in color. However, the color appears to ‘‘change’’ from blue to green to reddish.Interestingly, the Hadeda Ibis plumage also reflects ultraviolet and infrared while it isknown that only one animal, the Common Goldfish can detect both. Fig. 179a shows ascanning electron micrograph of iridescent feather of Hadeda Ibis and Fig. 179b is a trans-mission electron micrograph of cross-section of a single barbule. The barbules are rotatedby 90" so that the flattened surface reflects light normal to the contour of the Hadeda Ibis’sbody. The thickness of single barbule is 0.8 lm. Hollow melanosomes are visible in bar-bules by TEM. Unlike in other bird species, in Hadeda Ibis melanosomes only play aminor role, only to define the thick keratinous cortex in the production of structural color.Interference at the boundaries of the unusually thick keratinous cortex is responsible forthe iridescence of the feather [323].

Fig. 178. Schematic drawing showing (a) the structure of the vanes on the surface of scales ofM. rhetenor and (b)constructive interference in the ridges (from Nassau [319]).


Structural colors in biological systems are due to thin film interference involving well-defined multilayer structure or else coherent scattering from photonic arrays. The layersmay be composed of chitin as in wings of butterfly or keratin as in avian plumage color-ation as discussed. Other examples of structural coloration in nature include calcium car-bonate films in mother of pearl, chitin films in iridescent cuticle of beetles, andmelanosome platelets in hummingbird [320].

10.3. Chameleon

We have seen earlier that a-keratin is mammalian, whereas b-keratin is avian; the epi-dermis of the reptilian is unique, consisting of both a-and b-keratin. Metachrosis (chang-ing color) in lizard is the most famous and complex feature in reptile family [324]. The

Fig. 179. (a) Scanning electron micrograph of Hadeda Ibis feather; (b) transmission electron micrograph ofcross-section of barbules (from Brink and van der Berg [323, p. 809, Fig. 1]).


structure of the chameleon skin consists of several layers. The thin outermost layer of ober-hautchen consists of cornified cells with spinules throughout its surface. This covers athicker b layer which decreases in thickness along its hinges [325,326]. Fig. 180 showsthe cross-section of epidermis of the American chameleon (Anolis carlinensis) and themeso-layer between the a-layer and b-layer [325]. Below the a-layer, the structure is similarto a mammalian epidermis. The chameleon has pigment-containing cells called chromato-phores, embedded in the dermal layers. The chromatophores allow the chameleon tochange its skin color. Two or three kinds of pigments have been detected in the body ofthe American chameleon [328] while the African chameleon has five pigments. Fig. 181shows vertically sectioned back scale of American chameleon [327]. The hexagonal scaleof epidermis varies with position from 250 lm to 400 lm. There are two types of chro-matophores containing yellow pigment (xanthophore) and red pigments (erythrophore).The xanthophore (cells containing yellow pigment) layer lies under the stratum germinat-ivum layer, providing 10 lm of the dermal layer [327]. There is a 10–20 lm in thickness ofiridophore layer below the xanthophore layer. This contains inorganic crystalline pelletsthat reflect blue or white light. Erythrophores (cells containing red pigment) have beenfound in the basal zone of the iridophore layer of American chameleon [327]. Fig. 182shows iridophore platelets in the iridophore layers. The crystalline structure of iridophoreplatelets yields blue-green light [329]. The melanophores, which contain melanin, are thelargest of the chromatophores. These produce black or brown colors. This layer is fol-lowed by the iridophore layer which reaches the xanthophore layer [327]. The collagenousbasement lamella lies at the bottom of dermal layer. The skin color is controlled by theexpansion or contraction of the chromatophores producing a variety of colors from thedi!erent combination of chromatophore. The light modulation of color is provided bythe melanophores. Although the chameleon does contain any green pigmentation, the yel-low pigment and the reflecting blue light at iridophore layer produce the green color of theskin.

Fig. 180. Cross-Section of epidermis of American Chameleon. O: oberhautchen layer, B: beta layer, M: mesoslayer, A: alpha layer (from Alexander and Parakkal [325, Fig. 1]).


11. Bioinspired materials

Natural selection provides a tool with which nature has processed, improved, andrefined biologically-based elements over millions of years. As scientists we can learn fromthese evolutionary refinements and use them with the intention of creating novel improve-ments in technology. Materials Science is beginning to explore the resources presented by

Fig. 181. Cross-section of integument of American chameleon. Co: stratum corneum, G: stratum germinativum,P: xanthophore layer, C: carotenoid containing cell, I: iridophore, M: melanophore layer, L: collagenousbasement lamella (from Alexander and Fahrenbach [327, p. 47, Fig. 2]).


nature and use them to create novel advances in technology [330–333]. This interdisciplin-ary synergy between is the field of Biomimetics [4,6].

The production of inorganic materials in nature generally occurs at ambient tempera-ture and pressure under isothermal and isobaric conditions. Yet the simple organismsthrough which these inorganic materials are formed create extremely precise and complexstructures with advanced functionality [228]. Furthermore, the constituent materials pro-vided in nature are often brittle and weak. Thus, the strength of hard tissues such as shellsor bones is derived from the structure rather than through materials selection. As materialselection reaches its limitations, engineers look toward nature’s example of structural opti-mization for the next generation of technology.

There have been two approaches in generating bioinspired materials and structures. Itcan be hardly argued that all early attempts at flying were inspired most rather probablyby birds. The Greek legend of Icarus comes to mind. This traditional approach has utilizedsynthetic materials to produce performance that mimicks biological materials. Many ofthe early biomaterials (Vitallium, gold, etc.) are based on this approach. This will be dis-cussed in Section 11.1. The current frontier in bioinspired materials goes further and usesbioinspired processes at the molecular level to generate new materials and structures. Suchis the case of tissue engineering and other molecular-based approaches. Some of thesee!orts are presented in Section 11.2.

11.1. Traditional biomimetics

11.1.1. Aerospace materialsThe e!ect of gravity applies to both technology and nature as can be seen in the design

characteristics of biological avian materials such as bird beaks and bones. There is an

Fig. 182. Light micrograph of iridophore crystals (marked I) from American chameleon skin (from Rohrlich andRubin [329, p. 632, Fig. 1]).


apparent optimization of weight to strength through sandwich structures consisting ofsolid shells filled with compliant cellular cores [12,13]. The core significantly increasesthe buckling capabilities of the entire system while maintaining the light weight requiredfor flight. This synergism between a hard shell and a compliant core is also exhibited inother biological structures which require resistance against axial buckling. Plant stemsare an example of this, often consisting of thin-walled cylindrical structures filled with acellular core [334,335]. Their large aspect ratio creates an interesting engineering problemwhich has been posed both in nature and technology. Fig. 183 provides an examples of thisstructure in nature: a grass stem.

Birds have structures that are optimized for weight, and Fig. 184a shows the metacarpalbone in a vulture wing. This bone has a unique structure composed of two layers con-nected by a tridimensional array of inclined struts. This structure provides the sti!nessrequired by minimizing weight, since most of the mass is displaced away from the neutralplane. Interestingly, researchers are developing structures that are very similar (Fig. 184b).

Fig. 183. Cross-section of grass stem (Elytrigia repens) showing a shell structure with a foam-like core (fromKaram and Gibson [337]).


The example shown in Fig. 184b was developed for an experimental multifunctional mate-rial. This is a clear example of modern research finding solutions that have been applied bybiological systems for millions of years.

Karam and Gibson examined the elastic buckling of thin cylindrical shells filled withcompliant elastic cores [335–337]. Their results confirmed the benefit of the hard shell –elastic core synergy. Again, nature’s design stood up to the test, showing significantmechanical improvement with limited weight gain. Furthermore, the problem of axialbuckling in structures with high aspect ratios is approached as such materials and struc-tures are commonly found in both nature and technology.

11.1.2. Building designsOther examples of buckling resistance can be found throughout the natural world; even

the deepest parts of the ocean can accommodate organisms with interesting biomimeticpotential. The skeleton of a sea sponge, for example, exhibits amazing hierarchical levelsof complexity, each providing the essential components of structural design necessary forthe conversion of the otherwise brittle constituent material (silica) into a sophisticatedmasterpiece of architectural evolution. This structure has been studied to expose someof the engineering lessons which have stood the test of time over millions of years[40,94]. Fig. 185 shows a section of the skeleton of the sponge Euplectella [94]. Fig. 34shows the sea sponge in its entirety. The cylindrical cage extends 20–25 cm in lengthand 2–4 cm in diameter. The frame of the cage consists of long vertical struts runningthe entire length of the structure. Horizontal struts form a regular square lattice with

Fig. 184. (a) Metacarpal bone from a vulture’s wing. The structure is sti!ened by V-shaped struts in a 3-Dconfiguration (from Thompson [1, p. 976, Fig. 460]). (b) A CAD image of the truss core structure. Themultifunctional cellular metals has a similar structure to the metacarpal bone of vulture (from Evans et al. [348, p.319, Fig. 11a]).


the vertical struts. This structure is reinforced by external ridges that extend o! of the sur-face of the cylinder and spiral the cage at an angle of 45" to the cross-sectional plane. Abrittle material loaded in torsion will fail along the surface where tensile stresses are themaximum. This occurs 45" to the cross-sectional plane resulting in helical fractures[161]. The helical reinforcement of the cage is no accident of nature; the spiraling strutso!er important strengthening mechanisms to combat the destructive forces appliedthrough the ocean’s currents. Many similar reinforcements can be seen in advanced struc-tural engineering masterpieces including the Swiss Re Tower in London, Hotel De LasArtes in Barcelona, Spain and the Ei!el Tower in Paris as can be seen in the inserts ofFig. 185 (taken from Bell Labs).

11.1.3. Fiber optics and micro-lensesStructural reinforcement of this deep sea sponge is not limited to its macro-level design

described earlier. Each strut of the cage is composed of bundles of silica spicules. Thesespicules, that were discussed in detail in Section 6.1, consisting almost entirely silica, exhi-bit remarkable flexibility and toughness. Unlike their commercial counterparts, they canbe bent and tied into knots without fracture. This is attributed to the concentric lamellarstructure. Cylindrical layers, 0.2–1.5 lm thick are separated by extremely thin organicinter-layers shown in Fig. 186 [94]. This style of interplay between hard and soft materialscan be seen throughout the natural world. In almost all cases the laminate design of brittleinorganic layers separated by thin elastic regions of organic material leads to a dramaticincrease in toughness of otherwise weak materials. These organic regions are usually verysmall percent of entire composite. The optimization of composition and microstructure inthis natural material may inspire some novel improvements for its man made equivalent.

Fig. 185. Skeleton of the deep sea sponge Euplectella (from Aizenberg et al. [94]).


However the similarities between these two materials is not only limited to composition.The variation of reflective index of the various sections of the spicule results in wave-guid-ing properties similar to those found in modern fiber optics [95]. Described by Aizenberget al. [94], the cross-section in Fig. 186a shows three distinct regions: a core of pure silicasurrounding an organic filament, a central cylinder of high organic content, and the lam-inate layers with decreasing organic content. Interferometric refractive index profilingrevealed a high reflective index at the core surrounded by a low reflective index in the cen-tral cylinder. The ‘core-cladding’ profile in Fig. 186b shows how light can be confinedwithin the core and guided through the spicule. It is not clear whether the organism usesthe optical properties of the spicule, however in comparison to manmade counterparts thetechnical advantages are impressive.

The brittlestar is a marine animal that has great sensitivity to light. It was discovered byAizenberg and Hendler [338] that this organism, that does not have specialized eyes, has aset of lenses that channel light. These lenses focus the light 4–7 lm below the array, intothe neural bundles that exist in the animal. Fig. 187a shows these lenses. They have manyfeatures that are superior to synthetic microlenses. They minimize spherical aberration,

Fig. 186. Sponge spicule with (a) ‘core-cladding’ profile showing wave guiding properties, (b) commercial fiberoptics (from Sundar et al. [95]).


have a crystallographic orientation that eliminates birefringence, and contain an organic–inorganic composite that prevents the brittle calcium carbonate from fracturing easily.This brittlestar lens design was used at Bell laboratories to produce synthetic lenses mim-icking the properties. These synthetically produced microlens arrays have sub-10-lm poresand controlled crystallographic orientation. They are shown in Fig. 187b.

11.1.4. ManufacturingThe incredible control of nanoscaled material design in nature is unparalleled in current

technology [7,60,64]. As mentioned earlier, the sophisticated structures and materials arecreated in nature under ambient temperature and pressure. The man-made counterparts ofthese materials are typically produced under extreme conditions resulting in a myriad ofengineering obstacles which often times drive up the cost of production. Biomimeticallyinspired manufacturing techniques may result in the technical evolution of the way inwhich we think of manufacturing. Morse and coworkers [339] developed a manufacturingmethod for semiconductor thin films using inspiration from spicule formation. They foundthat by putting enzymes, similar to those of marine sponges, onto gold surfaces they couldcreate templates on which semiconductor films could grow. Using concepts of biomimeticscatalysts they were able to grow films at room temperature [340].

Fig. 187. (a) Brittlestar lenses; (b) synthetically produced microlens array (from Aizenberg and Hendler [338]).


Fig. 188. (a) Adult female, dorsal view; peaks and troughs are evident on the surface. (b) A ‘bump’ showinghydrophilic wax free region. (c) Scanning electron micrograph of the textured surface of the depressed areas. Scalebars, (a) 10 mm; (b) 0.2 mm; (c) 10 lm (from Parker and Lawrence [342]).


11.1.5. Water collectionEven the most extreme climates in the world can host animal life. The desert beetle, for

example, survives in one of the driest environments known to man. Extreme daytime tem-peratures, howling winds, and almost nonexistent rainfall leave desert areas almostentirely uninhabited. Yet every morning the tenebrionid bettle Stenocara sp. walksthrough a transitory fog, collecting essential drinking water on its back [341]. The bumpyback of beetle is designed to pull moisture from the air along alternating regions of hydro-phobic and hydrophilic surfaces [342]. Macro scaled bumps of approximately 0.5 mmdiameter pepper the back of the beetle as shown in Fig. 188a [342]. At the peak of eachbump a hydrophilic region protrudes into the surrounding atmosphere (Fig. 188b)[342]. The troughs between bumps and the sloping sides which descend from each peakare covered in wax. This area is equipped with a microstructure of tightly packed flattenedhemispheres 10 lm in diameter (Fig. 188c) [342]. As a result the surface of the back, withexception to the peak of each bump, is superhydrophobic. The hydrophilic peaks act asnucleation points for droplets to form from the surrounding moisture of the fog. As drop-lets grow to a critical size they slide o! of their unstable position at the peak of each bumpand into the hydrophobic troughs where they can roll down towards the mouth of thebeetle.

As a biomimetic material this type of functionality could be easily reproduced for com-mercial use [342]. Sheets of a similar structure could provide the essential drinking water tothe inhabitants of the extreme corners of the world.

11.1.6. VelcroOne of the most successfully commercialized biomimetic materials literally stuck itself

to its inventor’s pants. In the summer of 1948, the electrical engineer George de Mestralwas walking with his dog when he realized his pants had become covered in a plethoraof seed-bearing burrs. As he sat in frustration, tediously pulling burr after burr fromthe fabric of his clothes, curiosity grew in George’s mind. When he investigated the struc-ture of the burr under his microscope Mestral realized the secret to the seeds ability to

Fig. 189. Burs of a seed similar to the seed which gave birth to Velcro (from Armstrong [343]).


fasten themselves to many surfaces. It was tiny little hooks which covered the seed asshown in Fig. 189 [343]. From this Velours and Crochet ‘Velcro’ was born, giving riseto a multi-billion dollar industry.

11.1.7. Gecko feetAs seen in Section 10.1, tiny nanoscaled hairs known as spatulae line the bottom of a

gecko’s foot. They are used to create an electric bond with any surface they touch[312,344]. A Van der Waals attraction between individual atoms on the tip of each hairand the atoms on a surface is created. When millions of these hairs are all creating anattraction the combined force is great enough to keep the gecko tightly secured a wall.In fact the combined force theoretically could hold much more then just the weight of agecko. The unique attachment devices of geckos (Section 10.1) are being used as inspira-tion for synthetic devices. Artificial hair covered tapes made by engineers attempting tomimic the gecko’s foot promise to holds as much as 3 kilograms per cubic centimeter ofsurface area [345]. However these tapes, seen in Fig. 190, still lack the ability to truly recre-ate the ingenious design of nature. The artificial tapes tend to quickly become laden withwater or dust particles rendering them useless while the individual spatulae of the geckoare able to remain clean and reusable. This self-cleaning ability has yet to be successfullymimicked by man.

This work was first carried out by Sitti and Fearing [162], who produced synthetic poly-ethylene bristles by casting them from ceramic with nanoholes that had some of the prop-erties. However, they were marred with problems. The dashed line in Fig. 191 representsthe theoretical pull-o! strength obtained from Johnson–Kendall–Roberts equation [163].This gives the R&1/2 dependence of pullout strength. The experimental data (continuouslines) apply to synthetic pillar arrays manufactured by the Arzt group [312,357]. Thesearrays are shown in the photomicrographs at the corners of plot. Arrays with di!erentdiameters were produced, as shown in photographs. This is only a first e!ort, but the Ken-dall relationship between the pillar radius and the pull-out strength is obeyed.

Fig. 190. Biomimetic man made tape using gecko feet as inspiration (from Geim et al. [345]).


11.1.8. AbaloneThe first attempt at biomimicking dates back to the 1980s. A laminated structure of Al-

B4C was produced by Sarikaya and Aksay [140]. They demonstrated significant increasesin toughness. In Fig. 192, an increase in the fracture toughness of B4C (KIc ! 3 MPa m1/2)to about 16 MPa m1/2 was shown for the B4C-Al laminate. However, severe problemsoccurred because of the reaction of Al with B4C forming Al4C3, a very brittle material.Although improvements were achieved in the mechanical properties of synthetic laminatedcomposites [164,166,349] based on biological architecture, these have not been as extraor-dinary as the one nacre provides in comparison with monolithic CaCO3. This may be dueto limited laminate thickness in synthetic composites and the still not yet clearly identifiedcomposition and structure, especially of the complex nanolaminated structure in theorganic layer. Thus, the potential benefits of complex architectures have not been exploredfully yet. Nevertheless, research into bioinspired (specifically, abalone) armor continues.

Almqvist et al. [165] tried to reproduce the structure of the abalone by using tile withthe addition of a synthetic polymer as bonding. Tile has composition Mg3(Si4O10)(OH)2These particles have dimensions on the order of the CaCO3 tiles in abalone: a thicknessof a few hundred nanometer and diameter of 3–10 lm.

There is considerable industrial application of tile-polymer composites, with the poly-mer being more than 60 wt%. During extrusion, the particles orient themselves alongthe polymer flow direction. Almqvist et al. [165] attempted to reduce the polymer contentto less than 10% by aligning the tile particles though several techniques including sedimen-tation, centrifugation, shearing, and spinning. They encountered significant problems inwetting the tile particles with the polymer. They were not able to reproduce the high degree

Fig. 191. Pull-o! strength as a function of pillar radius (from Huber et al. [314]).


of order existing in nacre, although significant alignment of the tablets was achieved. Theyconcluded that the poor flexure strength achieved (in comparison with nacre) could beincreased by using a polymer with greater similarity to the viscoelastic organic componentin nacre.

There have been many other attempts at making microlaminates. Tang et al. [350,351]used electrical potential to sequentially deposit clay (montmorillomite) platelets and poly-mer chains and in this manner produced thin layers of a glue with the tiles arranged muchmore regularly than the ones produced by Almqvist et al. [165]. However, the sequentialdeposition on a silicon wafer substrate created layers that were only a few lm thick, sincethe individual Montmorillomite bricks had thicknesses of only 0.9 nm. This is seen inFig. 193a and b. There have also been macro scale attempts at biomimictry of abalonenacre. An example of this is provided in Fig. 193c. LAST# armor tiles, built by Foster–Miller (foster-miller.com), consist of SiC or B4C hexagonal tiles covered in a Kevlar# ther-moset laminate which are held together with a Velcro#-type adhesive. This nacre-likestructure provides energy absorption and toughening through many of the same mecha-nisms as its natural counterpart. The armor has been implemented onto various groundand air vehicles including over 1000 Humvees for the US Marines.

Manne and Aksay [352,353] considered other approaches to synthesizemicrolaminates:

(a) Langmuir–Blodgett (LB) deposition.The particles are floated on a water surfaceafter being coated with a hydrophobic layer.

(b) Covalent self-assembly.(c) Alternating sequential absorption.(d) Intercalation of organics into layered inorganic structures.

Fig. 192. Fracture toughness versus fracture strength of the nacre section of an Abalone shell compared to somehigh technology ceramic material (reproduced from Sarikaya et al. [134]).


A very innovative approach was recently demonstrated by Deville et al. [354,355]. Theyused the directional growth of ice crystals (dendrites) from a surface as the basis of theirsynthesis technique. As the ceramic slurry is frozen, the ice crystals expel the ceramic par-ticles. Fig. 194 shows the ice crystals forming columns or lamellae. The layers are as thin as

Fig. 193. (a) Schematic illustration of the (P/C)n film structure. The thickness of each clay platelet is 0.9 nm. (b)Scanning electron microscopy of an edge of a (P/C)100 film. (adapted from Tang et al. [350]). (c) LAST# armorbuilt by Foster–Miller (Foster-miller.com).


1 lm. The porous ceramic sca!olds formed by sublimation of the ice are then filled witheither a polymeric or metallic phase. Deville et al. [354,355] used hydroxyapatite as theceramic phase and were able to achieve a controlled porosity. The mechanical strengthof the porous skeleton (without infiltration of metal or ceramic) was significantly superiorto that of porous hydroxyapatite produced by other techniques (Fig. 195).

As seen in Section 6.1, marine sponges and other organisms produce silica via aqueousbio-mediated methods. This approach inspired Schwanzer et al. [356] to grow ZnO thinfilms. These ZnO films are conventionally grown by MOCVD, PLD, or MBE; they havea unique combination of optoelectronic, piezoelectronic properties, and are transparent.Schwanzer et al. [356] successively grow ZnO and Zn5(OH)8(NO3)32H2O thin films(including ITO coated glass) on di!erent substrates using an aqueous approach that mim-ics the biosilicification of marine sponges.

11.1.9. Marine adhesivesWhen developing an anchoring system for marine vessels, why not look at the systems

which have truly stood the test of time? The tides of the oceans have provided a tumultu-ous environment of marine life since the beginning of life on this earth. Organisms such asthe common mussel have been forced to develop remarkable methods of attaching them-selves onto structures in order to avoid being swept out to an inevitable and gruesomedeath. The mussel byssus threads seen in Fig. 196 are 5 times tougher and 16 times more

Fig. 194. Schematic illustration of the LBL synthesis of laminates through the growth of ice crystals (icetemplate, IT).


Fig. 195. Comparison of conventional porous hydroxyapatite and material produced by ice template (IT)method (reproduced from Deville et al. [354,355]).

Fig. 196. Mussel Byssus threads which provide the anchoring system for this marine organism (from Holl et al.[346]).


extensible then the human tendon [346,347], furthermore the natural glue which attacheseach thread to a surface is stronger then any man-made marine adhesive [258]. They aredescribed in greater detail in Section 8.4. The creation of commercial materials with theseproperties could be possible after first understanding the mechanisms with which natureproduces them.

Fig. 197. (a) Formation of a 2-D lattice from a junction with sticky ends. X and Y are sticky ends and X 0 and Y 0

are their complements. Four of the monomers assemble the structure on the right (reproduced from Seeman andBelcher [358]). (b) Self-assembled monolayers (SAMs) of alkanethiols can be formed on gold evaporated onto asolid flat substrate such as silicon or glass. The sulfur groups interact covalently with the gold, the poylmethylenechains pack tightly to form the monolayer, and the head groups are exposed (from Whitesides [37, p. 61, Fig. 3]).(c) Near-field phototlithography with self-assembled microlenses (from Whitesides [37, p. 61, Fig. 8]).


11.2. Molecular-based biomimetics

Aragonite and hydroxyapatite growth are, as seen in Section 6, complex processesincluding proteins and self-assembly. The current frontier in bio-inspired materials goesbeyond copying the structural elements. It starts at the nanometer level, with geneticallyengineered proteins; it also seeks to form the structures by self-assembly of its components.This field of research is still in its infancy but has enormous potential.

An example of the e!ect that genetic modification is the work by Snead et al. [185].They demonstrated in dental enamel that the self-assembly of proteins called amelogenininto nanospheres provides the environment from which hydroxyapatite crystals grow inthe woven pattern shown in Fig. 95b. By changing the amelogenin, transgenic mice wereproduced that had teeth where the enamel was less hard and exhibited a di!erent structure.This was accomplished by genetic engineering, which consisted of altering or deletingamino acids in the two highly conserved domains of mouse amelogenin.

The process of self-assembly is the essential component of the bottom-up approachthough which biological systems are formed. This process can be one-, two-, or three-dimensional. Fig. 197a illustrates how a two-dimensional network of branched DNA mol-ecules, in the form of a cross with ‘‘sticky’’ ends (left-hand side), can self-assemble to forma reticulated network (right hand side) [358]. This is just an illustration, and many morecomplex arrays are possible, depending on the functionality of the bonds. The possibleapplications of the DNA lattice shown in Fig. 197a are

• Sca!olding to crystallize biological macromolecules.• Organization of compounds in nanoelectronics.• Bio-inspired nano-component chips (quantum dots).

Whitesides and coworkers have pioneered self-assembled structures and used a numberof approaches. The early experiments on self-assembled monolayers (SAMs) by Nuzzoand Allara [51] inspired Bain and Whitesides [37,359] to use molecules with sulfur termi-nations. The sulfur atoms bond to the gold substrate and the molecules therefore form amonolayer. This is shown in Fig. 197b. The end of the molecule opposite to sulfur canhave a functional termination that changes the properties of the gold surface. For instance,if the end is a methyl group, the surface is hydrophobic. It the end is a carboxylic acidgroup, the surface is highly hydrophilic.

The Whitesides group [37,359,360] has also used 5 mm diameter balls (octahedrons withthe corners cut o!) with solder connections and shown that they can be self-assembled.After self-assembly, the solder of the junctions can be made to fuse them together. Thisis accomplished by placing the balls in a warm solution and tumbling them. If the solderdots, placed at specific facets, encounter one another, they fuse. If they encounter a surfacewith a LED, they do not fuse. After the assembly was completed, a current was passedthrough and the LEDs were lit. This approach illustrates the potential of using self-assem-bly to create electrical networks and represents a prototype for possible future. A photol-ithographic technique where the lenses are self-assembled is shown in Fig. 197c.

The bacteriophage (nicknamed ‘phage’) is a microbe that has nanoscale dimensions.Phages, like viruses, do not have reproductive organs. The T4 phage injects DNA intoE. coli bacteria. Fig. 198a shows the schematic representation of a phage that has an ico-sahedral head (capsid), a cylindrical tail sheath, and six legs. The scale of a T4 phage is


approximately 70 nm in diameter and 200 nm in length. It has unique properties which webriefly discuss below. The T4 phage, resembling a Mars Lander, connects to the membraneof a bacterium through the six legs. At that point, the tail sheath contracts and penetratesthe wall (Fig. 198b). This contraction is accomplished by a martensitic-like transformationin the tail sheath, as shown in Fig. 198c and as identified by Olson and Hartman [361,362].The contraction of the tail sheath propels a needle (tail core) through the bacterium wall.This enables the release of the DNA into the interior, where it uses the genetic machineryof the bacterium to reproduce itself.

The phages very simple: they consist of geometrical assemblies of DNA and a few pro-teins. There is no fatty tissue, no blood, no reproductive system. These components, oncemanufactured inside the bacterium, self-assemble. As the bacterium dies, the phages spew

Fig. 198. (a) A T4 Phage attaches to E. coli cell wall; (b) Insertion of the genetic material by a T4 phage. (c)Cylindrical crystal structure of virus tail-sheath during contraction by martensitic transformation. Interface isdescribed by coherency dislocations which spiral up helical close-packed crystal rows (reproduced from Olsonand Cohen [362]).


out and continue the cycle [34]. Phages can reassemble in a test tube after being broken upin a blender. This is shown in Fig. 199. This ability of phages to self-assemble in a quasi-mechanical way without any DNA templating or using proteins is inspiring scientists.Could this be used in the future?

Sarikaya and coworkers [53,332] used phages to find the proteins required for specificsurface interactions. Of special interest to materials scientists are protein interactions withinorganic substrates, such as silicon or gold. They used a technique from the molecularbiology field called phage display (PD) [53,332] to select proteins that bind to selected inor-ganic surfaces. This was based on earlier work by Brown [363], who found that some pro-teins selectively bind to specific inorganic surfaces. Sarikaya and coworkers [53,332]engineered new polypeptides that selectively bond to di!erent inorganic substrates:

Noble metals (Pt, Au, Ag, Pd).Metal oxides (ZnO, Al2O3, SiO2).Semiconductors (GaN, Cu2O, TiO2, ITO, Sulfides, Serenades).Other functional materials.

This method, that they call GEPI (Genetically Engineered Polypeptides for Inorganics)is represented in Fig. 200. The first step consists of obtaining random sequences of aminoacids by breaking up DNA. These are then incorporated into phages. These coated phagesare shown as step 2, Fig. 200. These phages are then exposed to the selected surface (step 3)and washed away (step 4). Several washes are required. The polypeptides that bind to theselected surface can not be removed by the washes, and are eluted (step 5). These polypep-tides are then replicated by having the phage inject the DNA into a bacterium. An attrac-tive methodology to PD is cell-surface display. There, the polypeptides are incorporatedinto cell surfaces. These genetically engineered polypeptides can potentially be used forgenerating a variety of nanoscale arrays on the surfaces of inorganics. These arrays havea range of applications; connected with the anchoring, coupling, branching, displaying,

Fig. 199. (a) The structure of the T4 bacteriophage; (b) Phage broken into parts can reassemble spontaneously.


and assembling of functional molecules, nanoparticles, and structures. The basic method-ology is illustrated in Fig. 201. Two di!erent GEPIs are used: GEPI-A and GEPI-B. Theyare assembled on a patterned substrate. Each GEPI is connected to an inorganic. Theseinorganics serve, on their turn, to attach functionalized monomers. These functionalizedmonomers can serve a variety of functions, such as conductors, photonic devices, or otherfunctions. Thus, the GEPIs can hypothetically serve as nanoscale platforms fornanoarrays.

Belcher [364] took the process one step further by using the phages directly to bind toZnS particles. The phages held the ZnS particles into position. Nanoscale ZnS particlescan, by this stratagem, produce regular arrays. Belcher’s [364] intended application for thisapproach is to create quantum dot devices.

Fig. 200. Method for obtaining genetically engineered polypeptides for inorganics (GEPIs) by phage display; (1)DNA is broken up into random sequences; (3) sequences are incorporated into phages; (4), (5) phages are put intocontact with inorganic surface and washed sequentially; (6) phages that stick to surface are eluted and have theirDNA injected into bacterium for expression replication (7); (9) exact DNA fragments (polypeptides) that stick tosurface are thus obtained; these are the famous GEPIs (adapted from Sarikaya et al. [332]).


In summary, the range of Biomimetic materials has barely been exposed. The develop-ment of novel technological advances could greatly benefit from the lessons taught by nature.Millions of years of trial and error have resulted in designs which are incomparably refined.

12. Summary and conclusions

The field of biological materials represents a growing component in Materials Scienceand Engineering. It is indeed one of its frontiers, since the first fifty years sinceMSE’s incep-tion have been devoted to metals, ceramics, polymers, and their composites in a unifiedway. The expansion into biological materials adds a level of complexity that is indeed achallenge that will stimulate an entire generation of researchers. The increased availabilityof nanoscale testing, characterization, and modeling methods has been and will continueprovide the tools required to advance our understanding of the behavior of structural bio-logical materials. The principal experimental and analytical tools are given below:

Nanoscale testing: nanoindentation, optical tweezers.Nanoscale characterization: TEM, AFM, Field Emission SEM.Nanoscale modeling: Molecular dynamics (MD).The unique and defining features of biological materials are:

(a) Self-assembly: They are first assembled at the molecular level; the structures are con-structed form the bottom up.

Fig. 201. The potential of using GEPI as ‘molecular erector’ sets. Two di!erent GEPI proteins (A and B) areassembled on ordered molecular or nanoscale substrates. The inorganic particles A and B are immobilizedselectively on GEPI-A and GEPI-B, respectively. Synthetic molecules are assembled using functionalized side-groups on the nanoparticles (reproduced from Sarikaya et al. [332]).


(b) Hierarchical structure: The structure varies in architecture with scale. The di!erenthierarchical levels operate in a synergistic fashion. In this monograph, we presentthe examples of tendon, nacreous layer of shells, arthropod exoskeleton, silk, dentin,and bone.

(c) Biological materials are, for the most, produced in an aqueous environment and atambient temperature.

(d) Multi-functionality: Many components in biological systems must have more thanone function, whereas synthetic systems often separate structural from functionalcomponent.

(e) Self healing: Most biological materials have built-in capacity to self-heal. This seemsto be a direct result of self-assembly, because the growth is not dictated from anoverarching scheme but occurs locally, from the bottom up, each molecule sensingits direct environment and responding to it.

Materials and design are intimately connected and inseparable in biological materials.This has traditionally not the case in man-made structures, where the process of designcalls for standard, o!-the-shelf, materials, and where the development of materials andevolution in design has often followed di!erent courses. A further defining characteristicof biological systems is that they are ‘‘grown’’, rather than ‘‘made’’ [365]. This is a directresult of self-assembly and is in contrast to many synthetic manufacturing processing inwhich the assembly of the component is dictated from a global plan. This has a profounde!ect on their structure, since they can undergo structural adjustments as the loads change.For example, a bone will undergo deposition in regions where the stresses are highest. Thesame happens in the growth of trees. The trunk and branches will thicken where the stres-ses are highest. This feature is called ‘‘adaptive mechanical design’’.

Nature accomplishes these functions of having a broad range of mechanical propertieswith a rather limited number of materials. The availability of materials in biological sys-tems is dictated by the two overarching constraints: ambient temperature and aqueousenvironment. Thus, it is the ingenious design of materials systems that produces the widerange of mechanical properties available to them.

The basic building blocks of soft biological materials are the 20 amino acids which pro-duce chains, called polypeptides. These polypeptide chains are the base for proteins. Thename protein comes from the Greek Proteios, which means ‘‘primary’’ or ‘‘first’’. Struc-tural proteins are the long molecular chains that, through their hierarchical organization,produce a range of elastic sti!ness and strength: collagen, keratin, elastin, resilin, chitin,actin, myosin, and abductin are the most important structural proteins. There are alsoproteins in tri-dimensional networks: hemoglobin and myoglobin are examples. In addi-tion to polypeptides, polysacchrides are the building blocks for chitin and cellulose.

Many hard biological materials (shells, bone, teeth, and crustacean exoskeleton) con-tain a mineral phase. This mineral phase is embedded in an organic (collagen) matrix inbone and dentin. In gastropod and bivalve shells (e.g. abalone), the mineral aragoniteforms tiles with dimensions of !10 lm · 0.5 lm and these are separated by thin(!50 nm) layers of organic. Some of the larger shells, the S. gigas, exhibit a greater degreeof mineralization with a more extensive growth of aragonite, while others (the conus fam-ily) exhibits a tessellated organization of the shells.

The mechanical strength of mineralized biological materials is connected to its nano-structure and to the scale, which limits the sizes of existing flaws to the level close to


the theoretical strength of the mineral. This was recently demonstrated by Gao et al. [149].However, this is only part of the story, and hierarchical aspects play a key role. In bone,crack bridging, which occurs on the scale of !20 lm, is utmost importance in determiningthe toughness, as pointed out by Nalla et al. [180]. In conch, the scale is even larger, on theorder of millimeters [194].

An important class of biological materials is cellular, i.e. they have a structure akin tofoam. Such is the case of trabecular bone, the inside of bird beaks, wood, hedgehog spikes,and plant stems. The presence of a cellular core is for the most part of a structure contain-ing a solid shell. These structures are designed to minimize the weight while maximizingthe sti!ness.

Two goals of Materials Scientists to study biological materials:

(a) The ‘materials’ approach of connecting the (nano-, micro-, meso-) structure to themechanical properties is di!erent from the viewpoint of biologists and chemists,since it analyses them as mechanical systems. This has yielded novel results and ishelping to elucidate many aspects of the structure here to fore not understood.

(b) The ultimate goal of synthesizing bioinspired structures is a novel approach withinthe design and manufacture. This approach has yielded some early successes suchas Velcro (the well known hook-loop attachment device) in which the material com-ponents were conventional and their performance was biomimicked.

A new direction consists of starting at the atomic/molecular level (bottom-upapproach) through self-assembly and to proceeds up in the dimensional scale, incorporat-ing the hierarchical complexity of biological materials. This approach is at the confluenceof biology and nanotechnology and is already yielding new architectures that have poten-tial applications in a number of areas, including quantum dots, photonic materials, drugdelivery, tissue engineering, and genetically engineered biomaterials.

Acknowledgements

This research is funded by the National Science Foundation Division of Materials Re-search, Biomaterials Program (Grant DMR 0510138). We gratefully acknowledge supportfrom Dr. Lynnette D. Madsen, Program Director, Ceramics and Dr. Joseph A. Akkara,Program Director, Biomaterials. The help provided by Dr. Chris Orme, LLNL, is greatlyappreciated. The inspiration provided by Prof. George Mayer, U. of Washington, andProf. Gareth Thomas, UC Berkeley is deeply appreciated. They insisted, for many yearsthat Marc A. Meyers should enter into this field. Dr. M. Mace, Curator of Birds at theSan Diego Zoo’s Wild Animal Park, kindly provided us with hornbill beaks. Mr. JerryJenkins, owner of Emerald Forest Bird Gardens, has helped us immensely with the toucanbeaks. Evelyn York, Scripps Institution of Oceanography, generously contributed withnumerous SEM sessions; Eddie Kisfaludy fed the abalone and kept them healthy. Finally,we owe a great dept of gratitude to Professor J. M. McKittrick, for encouraging and lovelydiscussions. Cristina Windsor, nee Meyers obtained the horseshoe crab specimen from theLong Island shores. Marc H. Meyers initiated the interest of his father in this field throughlong discussions and joint work on abalone. Sara Bodde kindly provided the SEM micro-graphs of bird feathers and contributed to that section. Discussions with Profs. V. Lubar-da and K.S. Vecchio were extremely helpful.


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